<<< native
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, EDelimited "(" ")" [ Right (EIdentifier "z") ]
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]
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, []
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[ EGrouped
[ EGrouped
[ ESuper (EIdentifier "z") (ENumber "2")
, ESymbol Ord "\8290"
, EFraction
NormalFrac
(EGrouped
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(EGrouped
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NormalFrac
(EGrouped [ ESymbol Ord "\8518" , EIdentifier "w" ])
(EGrouped [ ESymbol Ord "\8518" , EIdentifier "z" ])
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, ESymbol Bin "\8722"
, EGrouped
[ EDelimited
"("
")"
[ Right
(EGrouped
[ ESuper (EIdentifier "z") (ENumber "2")
, ESymbol Bin "+"
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, ESymbol Ord "\8290"
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, []
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[ EGrouped
[ EFraction
NormalFrac
(EGrouped
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[ EIdentifier "u"
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(EGrouped
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, EFraction
NormalFrac
(EGrouped
[ ESuper (ESymbol Ord "\8706") (ENumber "2")
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[ EIdentifier "u"
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[ ESymbol Open "("
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(EGrouped
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[ EGrouped
[ EIdentifier "y"
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, EDelimited
"("
")"
[ Right
(EGrouped [ EIdentifier "t" , ESymbol Pun "," , EIdentifier "x" ])
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]
, ESymbol Rel "="
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[ EGrouped
[ ESub (EIdentifier "F") (ENumber "1")
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"("
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[ Right
(EGrouped
[ EGrouped [ ESymbol Bin "\8722" , EIdentifier "x" ]
, ESymbol Bin "\8722"
, EGrouped
[ EIdentifier "a" , ESymbol Ord "\8290" , EIdentifier "t" ]
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, ESymbol Bin "+"
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[ ESub (EIdentifier "F") (ENumber "2")
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, EDelimited
"("
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[ Right
(EGrouped
[ EIdentifier "x"
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[ EIdentifier "a" , ESymbol Ord "\8290" , EIdentifier "t" ]
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, []
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, [ [ EArray
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, []
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[ [ [ EGrouped
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[ EGrouped
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, EIdentifier "y"
, ESymbol Bin "\8722"
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]
, ESymbol Rel "="
, ENumber "98"
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, []
]
, [ [ EArray
[ AlignCenter ]
[ [ [ EGrouped
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]
]
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, [ [ EArray
[ AlignCenter ]
[ [ [ EGrouped
[ EGrouped
[ ESub (EIdentifier "A") (ENumber "1")
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[ EGrouped
[ ESub (EIdentifier "N") (ENumber "0")
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, ESymbol Bin "\8722"
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[ EIdentifier "\966"
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[ ESymbol Open "("
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[ ESub (EIdentifier "A") (ENumber "2")
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[ EGrouped
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[ ESymbol Open "("
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[ EIdentifier "\955"
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[ EIdentifier "\966"
, ESymbol Ord "\8289"
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[ ESymbol Open "("
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[ EIdentifier "\955"
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[ EStyled TextScript [ EIdentifier "N" ]
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[ ESymbol Open "("
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[ [ [ EGrouped
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, [ [ EGrouped
[ EIdentifier "x"
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""
[ Right
(EArray
[ AlignLeft , AlignLeft ]
[ [ [ EIdentifier "x" ]
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[ EText TextNormal "if\8194"
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, [ EGrouped
[ EText TextNormal "if\8194"
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[ [ [ EGrouped
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, EIdentifier "M"
, ESymbol Ord "\8290"
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, ESymbol Ord "\8290"
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, EIdentifier "M"
, ESymbol Ord "\8290"
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, []
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, [ [ EArray
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, EIdentifier "A"
, ESymbol Ord "\8290"
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, ESymbol Ord "\8290"
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, []
]
, [ [ EGrouped [ EMathOperator "\8711\183" , EIdentifier "F" ] ]
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]
, [ [ EGrouped
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[ EGrouped
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[ EGrouped
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[ EGrouped
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, EGrouped [ ESymbol Bin "\8722" , ENumber "1" ]
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, [ [ EGrouped
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, []
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, [ [ EGrouped [ EIdentifier "x" , ESymbol Bin "+" , ENumber "1" ]
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, [ [ EGrouped
[ EGrouped
[ EIdentifier "x"
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[ EIdentifier "f"
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, []
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[ EGrouped
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, ESymbol Ord "\8290"
, EStyled TextItalic [ EIdentifier "h" ]
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, EStyled TextItalic [ EIdentifier "e" ]
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, ESymbol Ord "\8290"
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, EIdentifier "f"
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, ESymbol Ord "\8290"
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, ESymbol Ord "\8290"
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, ESymbol Ord "\8290"
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, ESymbol Ord "\8290"
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, ESymbol Ord "\8290"
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, ESymbol Ord "\8290"
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, ESymbol Ord "\8290"
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, ESymbol Ord "\8290"
, EStyled TextSansSerif [ EIdentifier "a" ]
, ESymbol Ord "\8290"
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, ESymbol Ord "\8290"
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, EIdentifier "e"
, ESymbol Ord "\8290"
, EIdentifier "n"
, ESymbol Ord "\8290"
, EIdentifier "d"
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, []
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"("
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[ Right
(EGrouped
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[ EFraction
NormalFrac
(EGrouped [ ESymbol Ord "\8706" , EIdentifier "f" ])
(EGrouped
[ ESymbol Ord "\8706" , ESub (EIdentifier "x") (ENumber "1") ])
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"("
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NormalFrac
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(EGrouped
[ ESymbol Ord "\8706" , ESub (EIdentifier "x") (ENumber "2") ])
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"("
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NormalFrac
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"("
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"("
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[ EIdentifier "c" , ESymbol Ord "\8290" , EIdentifier "v" ]
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[ EIdentifier "f"
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"("
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[ EGrouped
[ EGrouped
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NormalFrac
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"("
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(EGrouped
[ EIdentifier "a"
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NormalFrac
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"("
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NormalFrac
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"("
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(EGrouped
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, []
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[ EGrouped
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(EGrouped
[ EIdentifier "\960"
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[ ENumber "2"
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"("
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[ Right
(EGrouped
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[ EFraction NormalFrac (ENumber "1") (ENumber "7")
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, Left "|"
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(EGrouped
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, ESymbol Pun ","
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[ EIdentifier "\952"
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"{"
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[ Right
(EGrouped
[ EGrouped
[ ENumber "2"
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, ESymbol Ord "\8290"
, EIdentifier "\960"
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"("
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[ Right
(EGrouped
[ EMathOperator "arccos"
, ESymbol Ord "\8289"
, EGrouped
[ EFraction NormalFrac (ENumber "1") (ENumber "7")
, ESymbol Ord "\8290"
, ESqrt (ENumber "14")
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, Left "|"
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(EGrouped
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, EIdentifier "\8484"
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, []
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, [ [ EGrouped
[ EIdentifier "P"
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[ EIdentifier "A"
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, ESuper
(EDelimited
"("
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[ Right
(EGrouped
[ ESuper (EIdentifier "A") (EIdentifier "T")
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, EIdentifier "A"
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(EGrouped [ ESymbol Bin "\8722" , ENumber "1" ])
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, ESuper (EIdentifier "A") (EIdentifier "T")
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]
]
, []
]
, [ [ EGrouped
[ EGrouped
[ EMathOperator "det"
, EDelimited
"("
")"
[ Right
(EArray
[ AlignCenter , AlignCenter , AlignCenter ]
[ [ [ EIdentifier "x" ] , [ EIdentifier "y" ] , [ ENumber "1" ] ]
, [ [ EIdentifier "a" ] , [ EIdentifier "b" ] , [ ENumber "1" ] ]
, [ [ EIdentifier "a" ] , [ EIdentifier "d" ] , [ ENumber "1" ] ]
])
]
]
, ESymbol Rel "="
, EGrouped
[ EGrouped
[ EIdentifier "x" , ESymbol Ord "\8290" , EIdentifier "b" ]
, ESymbol Bin "\8722"
, EGrouped
[ EIdentifier "x" , ESymbol Ord "\8290" , EIdentifier "d" ]
, ESymbol Bin "+"
, EGrouped
[ EIdentifier "a" , ESymbol Ord "\8290" , EIdentifier "d" ]
, ESymbol Bin "\8722"
, EGrouped
[ EIdentifier "a" , ESymbol Ord "\8290" , EIdentifier "b" ]
]
, ESymbol Rel "="
, ENumber "0"
]
]
, []
]
, [ [ EGrouped
[ EGrouped
[ EGrouped
[ EIdentifier "A"
, ESymbol Ord "\8289"
, EDelimited "(" ")" [ Right (EIdentifier "\952") ]
]
, ESymbol Ord "\8290"
, EGrouped
[ EIdentifier "A"
, ESymbol Ord "\8289"
, EDelimited
"("
")"
[ Right (EGrouped [ ESymbol Bin "\8722" , EIdentifier "\952" ]) ]
]
]
, ESymbol Rel "="
, EGrouped
[ EDelimited
"["
"]"
[ Right
(EArray
[ AlignCenter , AlignCenter ]
[ [ [ EGrouped
[ EMathOperator "cos"
, ESymbol Ord "\8289"
, EIdentifier "\952"
]
]
, [ EGrouped
[ ESymbol Bin "\8722"
, EGrouped
[ EMathOperator "sin"
, ESymbol Ord "\8289"
, EIdentifier "\952"
]
]
]
]
, [ [ EGrouped
[ EMathOperator "sin"
, ESymbol Ord "\8289"
, EIdentifier "\952"
]
]
, [ EGrouped
[ EMathOperator "cos"
, ESymbol Ord "\8289"
, EIdentifier "\952"
]
]
]
])
]
, ESymbol Ord "\8290"
, EDelimited
"["
"]"
[ Right
(EArray
[ AlignCenter , AlignCenter ]
[ [ [ EGrouped
[ EMathOperator "cos"
, ESymbol Ord "\8289"
, EIdentifier "\952"
]
]
, [ EGrouped
[ EMathOperator "sin"
, ESymbol Ord "\8289"
, EIdentifier "\952"
]
]
]
, [ [ EGrouped
[ ESymbol Bin "\8722"
, EGrouped
[ EMathOperator "sin"
, ESymbol Ord "\8289"
, EIdentifier "\952"
]
]
]
, [ EGrouped
[ EMathOperator "cos"
, ESymbol Ord "\8289"
, EIdentifier "\952"
]
]
]
])
]
]
]
]
, []
]
, [ [ EGrouped
[ EGrouped
[ EIdentifier "J"
, ESymbol Ord "\8289"
, EGrouped
[ ESymbol Open "(" , EIdentifier "A" , ESymbol Close ")" ]
]
, ESymbol Rel "="
, EDelimited
"["
"]"
[ Right
(EArray
[ AlignCenter , AlignCenter , AlignCenter , AlignCenter ]
[ [ [ EGrouped
[ ESub (EIdentifier "J") (ESub (EIdentifier "n") (ENumber "1"))
, ESymbol Ord "\8289"
, EDelimited
"(" ")" [ Right (ESub (EIdentifier "\955") (ENumber "1")) ]
]
]
, [ ENumber "0" ]
, [ EIdentifier "\8943" ]
, [ ENumber "0" ]
]
, [ [ ENumber "0" ]
, [ EGrouped
[ ESub (EIdentifier "J") (ESub (EIdentifier "n") (ENumber "2"))
, ESymbol Ord "\8289"
, EDelimited
"(" ")" [ Right (ESub (EIdentifier "\955") (ENumber "2")) ]
]
]
, [ EIdentifier "\8943" ]
, [ ENumber "0" ]
]
, [ [ EText TextNormal "\8942" ]
, [ EText TextNormal "\8942" ]
, [ EText TextNormal "\8945" ]
, [ EText TextNormal "\8942" ]
]
, [ [ ENumber "0" ]
, [ ENumber "0" ]
, [ EIdentifier "\8943" ]
, [ EGrouped
[ ESub (EIdentifier "J") (ESub (EIdentifier "n") (EIdentifier "k"))
, ESymbol Ord "\8289"
, EDelimited
"(" ")" [ Right (ESub (EIdentifier "\955") (EIdentifier "k")) ]
]
]
]
])
]
]
]
, []
]
, [ [ EGrouped
[ EGrouped
[ EMathOperator "det"
, EDelimited
"("
")"
[ Right
(EArray
[ AlignCenter , AlignCenter , AlignCenter ]
[ [ [ EGrouped
[ EGrouped [ ESymbol Bin "\8722" , ENumber "4" ]
, ESymbol Bin "+"
, EIdentifier "X"
]
]
, [ EGrouped [ ESymbol Bin "\8722" , ENumber "1" ] ]
, [ ENumber "0" ]
]
, [ [ ENumber "0" ]
, [ EGrouped
[ EGrouped [ ESymbol Bin "\8722" , ENumber "4" ]
, ESymbol Bin "+"
, EIdentifier "X"
]
]
, [ ENumber "0" ]
]
, [ [ ENumber "0" ]
, [ ENumber "0" ]
, [ EGrouped
[ EGrouped [ ESymbol Bin "\8722" , ENumber "4" ]
, ESymbol Bin "+"
, EIdentifier "X"
]
]
]
])
]
]
, ESymbol Rel "="
, ESuper
(EDelimited
"("
")"
[ Right
(EGrouped [ EIdentifier "X" , ESymbol Bin "\8722" , ENumber "4" ])
])
(ENumber "3")
]
]
, []
]
, [ [ EDelimited
""
""
[ Right
(EDelimited
"{"
"}"
[ Right
(EDelimited
"("
")"
[ Right
(EArray
[ AlignCenter ]
[ [ [ EGrouped
[ EGrouped
[ ESymbol Bin "\8722"
, EFraction NormalFrac (ENumber "1") (ENumber "2")
]
, ESymbol Bin "\8722"
, EGrouped
[ EFraction NormalFrac (ENumber "1") (ENumber "6")
, ESymbol Ord "\8290"
, ESqrt (ENumber "33")
]
]
]
]
, [ [ ENumber "1" ] ]
])
])
])
, Left "\8596"
, Right
(EGrouped
[ EFraction NormalFrac (ENumber "5") (ENumber "2")
, ESymbol Bin "\8722"
, EGrouped
[ EFraction NormalFrac (ENumber "1") (ENumber "2")
, ESymbol Ord "\8290"
, ESqrt (ENumber "33")
]
])
]
]
, []
]
, [ [ EGrouped
[ EDelimited
"" "" [ Left "\8741" , Right (EIdentifier "A") , Left "\8741" ]
, ESymbol Rel "="
, EGrouped
[ EUnder
False
(EMathOperator "max")
(EGrouped [ EIdentifier "x" , ESymbol Rel "\8800" , ENumber "0" ])
, EFraction
NormalFrac
(EDelimited
""
""
[ Left "\8741"
, Right
(EGrouped
[ EIdentifier "A" , ESymbol Ord "\8290" , EIdentifier "x" ])
, Left "\8741"
])
(EDelimited
"" "" [ Left "\8741" , Right (EIdentifier "x") , Left "\8741" ])
]
]
]
, []
]
, [ [ EGrouped
[ EGrouped
[ EDelimited
"("
")"
[ Right
(EArray
[ AlignCenter , AlignCenter ]
[ [ [ ESub
(EIdentifier "a")
(EGrouped [ ENumber "1" , ESymbol Ord "\8203" , ENumber "1" ])
]
, [ ESub
(EIdentifier "a")
(EGrouped [ ENumber "1" , ESymbol Ord "\8203" , ENumber "2" ])
]
]
, [ [ ESub
(EIdentifier "a")
(EGrouped [ ENumber "2" , ESymbol Ord "\8203" , ENumber "1" ])
]
, [ ESub
(EIdentifier "a")
(EGrouped [ ENumber "2" , ESymbol Ord "\8203" , ENumber "2" ])
]
]
])
]
, ESymbol Bin "+"
, EDelimited
"("
")"
[ Right
(EArray
[ AlignCenter , AlignCenter ]
[ [ [ ESub
(EIdentifier "b")
(EGrouped [ ENumber "1" , ESymbol Ord "\8203" , ENumber "1" ])
]
, [ ESub
(EIdentifier "b")
(EGrouped [ ENumber "1" , ESymbol Ord "\8203" , ENumber "2" ])
]
]
, [ [ ESub
(EIdentifier "b")
(EGrouped [ ENumber "2" , ESymbol Ord "\8203" , ENumber "1" ])
]
, [ ESub
(EIdentifier "b")
(EGrouped [ ENumber "2" , ESymbol Ord "\8203" , ENumber "2" ])
]
]
])
]
]
, ESymbol Rel "="
, EDelimited
"("
")"
[ Right
(EArray
[ AlignCenter , AlignCenter ]
[ [ [ EGrouped
[ ESub
(EIdentifier "a")
(EGrouped [ ENumber "1" , ESymbol Ord "\8203" , ENumber "1" ])
, ESymbol Bin "+"
, ESub
(EIdentifier "b")
(EGrouped [ ENumber "1" , ESymbol Ord "\8203" , ENumber "1" ])
]
]
, [ EGrouped
[ ESub
(EIdentifier "a")
(EGrouped [ ENumber "1" , ESymbol Ord "\8203" , ENumber "2" ])
, ESymbol Bin "+"
, ESub
(EIdentifier "b")
(EGrouped [ ENumber "1" , ESymbol Ord "\8203" , ENumber "2" ])
]
]
]
, [ [ EGrouped
[ ESub
(EIdentifier "a")
(EGrouped [ ENumber "2" , ESymbol Ord "\8203" , ENumber "1" ])
, ESymbol Bin "+"
, ESub
(EIdentifier "b")
(EGrouped [ ENumber "2" , ESymbol Ord "\8203" , ENumber "1" ])
]
]
, [ EGrouped
[ ESub
(EIdentifier "a")
(EGrouped [ ENumber "2" , ESymbol Ord "\8203" , ENumber "2" ])
, ESymbol Bin "+"
, ESub
(EIdentifier "b")
(EGrouped [ ENumber "2" , ESymbol Ord "\8203" , ENumber "2" ])
]
]
]
])
]
]
]
, []
]
, [ [ EGrouped
[ EGrouped
[ EIdentifier "f"
, ESymbol Ord "\8289"
, EDelimited
"("
")"
[ Right
(EDelimited
"["
"]"
[ Right
(EArray
[ AlignCenter , AlignCenter ]
[ [ [ ENumber "1" ] , [ ENumber "2" ] ]
, [ [ ENumber "4" ] , [ ENumber "3" ] ]
])
])
]
]
, ESymbol Rel "="
, EGrouped
[ ESuper
(EDelimited
"["
"]"
[ Right
(EArray
[ AlignCenter , AlignCenter ]
[ [ [ ENumber "1" ] , [ ENumber "2" ] ]
, [ [ ENumber "4" ] , [ ENumber "3" ] ]
])
])
(ENumber "2")
, ESymbol Bin "\8722"
, EGrouped
[ ENumber "5"
, ESymbol Ord "\8290"
, EDelimited
"["
"]"
[ Right
(EArray
[ AlignCenter , AlignCenter ]
[ [ [ ENumber "1" ] , [ ENumber "2" ] ]
, [ [ ENumber "4" ] , [ ENumber "3" ] ]
])
]
]
, ESymbol Bin "\8722"
, ENumber "2"
]
, ESymbol Rel "="
, EDelimited
"["
"]"
[ Right
(EArray
[ AlignCenter , AlignCenter ]
[ [ [ ENumber "2" ]
, [ EGrouped [ ESymbol Bin "\8722" , ENumber "2" ] ]
]
, [ [ EGrouped [ ESymbol Bin "\8722" , ENumber "4" ] ]
, [ ENumber "0" ]
]
])
]
]
]
, []
]
, [ [ EGrouped
[ EIdentifier "x"
, ESymbol Rel "="
, EGrouped
[ EUnder
False
(EMathOperator "lim")
(EGrouped [ EIdentifier "x" , ESymbol Rel "=" , ENumber "1" ])
, EGrouped
[ EUnderover False (ESymbol Op "\8721") (ENumber "1") (ENumber "2")
, EIdentifier "a"
]
]
]
]
, []
]
, [ [ EGrouped
[ EGrouped
[ ESubsup (ESymbol Op "\8747") (EIdentifier "a") (EIdentifier "b")
, EGrouped
[ EGrouped
[ EIdentifier "f"
, ESymbol Ord "\8289"
, EGrouped
[ ESymbol Open "(" , EIdentifier "x" , ESymbol Close ")" ]
]
, ESymbol Ord "\8290"
, EGrouped [ ESymbol Ord "\8518" , EIdentifier "x" ]
]
]
, ESymbol Rel "="
, EGrouped
[ EUnder
False
(EMathOperator "lim")
(EGrouped
[ EGrouped
[ ESymbol Op "\8741" , EIdentifier "P" , ESymbol Op "\8741" ]
, ESymbol Accent "\8594"
, ENumber "0"
])
, EGrouped
[ EUnderover
False
(ESymbol Op "\8721")
(EGrouped [ EIdentifier "i" , ESymbol Rel "=" , ENumber "1" ])
(EIdentifier "n")
, EGrouped
[ EGrouped
[ EIdentifier "f"
, ESymbol Ord "\8289"
, EDelimited
"("
")"
[ Right
(ESub
(EOver False (EIdentifier "x") (ESymbol Accent "\175"))
(EIdentifier "i"))
]
]
, ESymbol Ord "\8290"
, EGrouped
[ ESymbol Alpha "\916" , ESub (EIdentifier "x") (EIdentifier "i") ]
]
]
]
]
]
, []
]
, [ [ EGrouped
[ EGrouped
[ ESubsup (ESymbol Op "\8747") (EIdentifier "a") (EIdentifier "b")
, EGrouped
[ EGrouped
[ EIdentifier "f"
, ESymbol Ord "\8289"
, EGrouped
[ ESymbol Open "(" , EIdentifier "x" , ESymbol Close ")" ]
]
, ESymbol Ord "\8290"
, EGrouped [ ESymbol Ord "\8518" , EIdentifier "x" ]
]
]
, ESymbol Rel "="
, EGrouped
[ EUnder
False
(EMathOperator "lim")
(EGrouped
[ EIdentifier "n" , ESymbol Accent "\8594" , EIdentifier "\8734" ])
, EGrouped
[ EFraction
NormalFrac
(EGrouped
[ EIdentifier "b" , ESymbol Bin "\8722" , EIdentifier "a" ])
(EIdentifier "n")
, ESymbol Ord "\8290"
, EGrouped
[ EUnderover
False
(ESymbol Op "\8721")
(EGrouped [ EIdentifier "i" , ESymbol Rel "=" , ENumber "1" ])
(EIdentifier "n")
, EGrouped
[ EIdentifier "f"
, ESymbol Ord "\8289"
, EDelimited
"("
")"
[ Right
(EGrouped
[ EIdentifier "a"
, ESymbol Bin "+"
, EGrouped
[ EIdentifier "i"
, ESymbol Ord "\8290"
, EFraction
NormalFrac
(EGrouped
[ EIdentifier "b"
, ESymbol Bin "\8722"
, EIdentifier "a"
])
(EIdentifier "n")
]
])
]
]
]
]
]
]
]
, []
]
, [ [ EGrouped
[ EGrouped
[ ESubsup (ESymbol Op "\8747") (ENumber "0") (ENumber "2")
, EGrouped
[ ESuper (EIdentifier "x") (ENumber "5")
, ESymbol Ord "\8290"
, ESqrt
(EGrouped
[ ESuper (EIdentifier "x") (ENumber "3")
, ESymbol Bin "+"
, ENumber "1"
])
, ESymbol Ord "\8290"
, EGrouped [ ESymbol Ord "\8518" , EIdentifier "x" ]
]
]
, ESymbol Rel "="
, EGrouped
[ ESubsup (ESymbol Op "\8747") (ENumber "1") (ENumber "3")
, EGrouped
[ EFraction NormalFrac (ENumber "2") (ENumber "3")
, ESymbol Ord "\8290"
, EIdentifier "u"
, ESymbol Ord "\8290"
, EFraction
NormalFrac
(ESqrt
(EDelimited
"(" ")" [ Right (ESuper (EIdentifier "u") (ENumber "2")) ]))
(ESuper
(EDelimited
"("
")"
[ Right
(EGrouped
[ ESuper (EIdentifier "u") (ENumber "2")
, ESymbol Bin "\8722"
, ENumber "1"
])
])
(EFraction NormalFrac (ENumber "2") (ENumber "3")))
, ESymbol Ord "\8290"
, EDelimited
"("
")"
[ Right
(EGrouped
[ EGrouped
[ ESuper (EIdentifier "u") (ENumber "2")
, ESymbol Ord "\8290"
, ESuper
(EDelimited
"("
")"
[ Right
(EGrouped
[ ESuper (EIdentifier "u") (ENumber "2")
, ESymbol Bin "\8722"
, ENumber "1"
])
])
(EFraction NormalFrac (ENumber "2") (ENumber "3"))
]
, ESymbol Bin "\8722"
, ESuper
(EDelimited
"("
")"
[ Right
(EGrouped
[ ESuper (EIdentifier "u") (ENumber "2")
, ESymbol Bin "\8722"
, ENumber "1"
])
])
(EFraction NormalFrac (ENumber "2") (ENumber "3"))
])
]
, ESymbol Ord "\8290"
, EGrouped [ ESymbol Ord "\8518" , EIdentifier "u" ]
]
]
]
]
, []
]
, [ [ EGrouped
[ EDelimited
"\8747"
""
[ Right
(EGrouped
[ EGrouped
[ EIdentifier "f"
, ESymbol Ord "\8289"
, EGrouped
[ ESymbol Open "("
, EGrouped
[ EIdentifier "g"
, ESymbol Ord "\8289"
, EGrouped
[ ESymbol Open "(" , EIdentifier "x" , ESymbol Close ")" ]
]
, ESymbol Close ")"
]
]
, ESymbol Ord "\8290"
, EGrouped
[ ESuper (EIdentifier "g") (ESymbol Ord "\8242")
, ESymbol Ord "\8289"
, EGrouped
[ ESymbol Open "(" , EIdentifier "x" , ESymbol Close ")" ]
]
, ESymbol Ord "\8290"
, EGrouped [ ESymbol Ord "\8518" , EIdentifier "x" ]
])
]
, ESymbol Rel "="
, EDelimited
"\8747"
""
[ Right
(EGrouped
[ EGrouped
[ EIdentifier "f"
, ESymbol Ord "\8289"
, EGrouped
[ ESymbol Open "(" , EIdentifier "u" , ESymbol Close ")" ]
]
, ESymbol Ord "\8290"
, EGrouped [ ESymbol Ord "\8518" , EIdentifier "u" ]
])
]
]
]
, []
]
, [ [ EGrouped
[ EIdentifier "x"
, ESymbol Rel "="
, EGrouped
[ ENumber "2"
, ESymbol Ord "\8290"
, EGrouped
[ EUnderover
False
(ESymbol Op "\8721")
(EGrouped [ EIdentifier "n" , ESymbol Rel "=" , ENumber "1" ])
(ENumber "100")
, EGrouped
[ EIdentifier "n"
, ESymbol Ord "\8290"
, EGrouped
[ ESymbol Open "("
, EGrouped [ EIdentifier "n" , ESymbol Bin "\8722" , ENumber "1" ]
, ESymbol Close ")"
]
]
]
]
]
]
, []
]
, [ [ EGrouped
[ EGrouped
[ EUnder
False
(EMathOperator "lim")
(EGrouped
[ EIdentifier "x" , ESymbol Accent "\8594" , ENumber "0" ])
, EGrouped
[ EMathOperator "sin"
, ESymbol Ord "\8289"
, EDelimited
"("
")"
[ Right (EFraction NormalFrac (ENumber "1") (EIdentifier "x")) ]
]
]
, ESymbol Rel "="
, EGrouped
[ EGrouped [ ESymbol Bin "\8722" , ENumber "1" ]
, ESymbol Ord ".."
, ENumber "1"
]
]
]
, []
]
, [ [ EGrouped
[ EGrouped
[ EIdentifier "h"
, ESymbol Ord "\8289"
, EGrouped
[ ESymbol Open "("
, EGrouped [ EIdentifier "i" , ESymbol Pun "," , EIdentifier "j" ]
, ESymbol Close ")"
]
]
, ESymbol Rel "="
, EGrouped
[ EGrouped
[ EGrouped
[ ESymbol Open "("
, EGrouped [ ENumber "2" , ESymbol Bin "\8722" , EIdentifier "j" ]
, ESymbol Close ")"
]
, ESymbol Ord "\8290"
, EGrouped
[ EIdentifier "g"
, ESymbol Ord "\8289"
, EGrouped
[ ESymbol Open "(" , EIdentifier "i" , ESymbol Close ")" ]
]
]
, ESymbol Bin "+"
, EGrouped
[ EGrouped
[ ESymbol Open "("
, EGrouped [ EIdentifier "j" , ESymbol Bin "\8722" , ENumber "1" ]
, ESymbol Close ")"
]
, ESymbol Ord "\8290"
, EGrouped
[ EIdentifier "f"
, ESymbol Ord "\8289"
, EGrouped
[ ESymbol Open "("
, EGrouped
[ EIdentifier "g"
, ESymbol Ord "\8289"
, EGrouped
[ ESymbol Open "(" , EIdentifier "i" , ESymbol Close ")" ]
]
, ESymbol Close ")"
]
]
]
]
]
]
, []
]
, [ [ EGrouped
[ EIdentifier "\9651"
, ESymbol Pun ":"
, EDelimited
""
""
[ Right
(EDelimited
"["
"]"
[ Right (EGrouped [ ENumber "0" , ESymbol Pun "," , ENumber "1" ])
])
, Left "\8594"
, Right
(EDelimited
"["
"]"
[ Right (EGrouped [ ENumber "0" , ESymbol Pun "," , ENumber "1" ])
])
]
]
]
, []
]
, [ [ EGrouped
[ EGrouped [ ENumber "0" , ESymbol Bin "\9661" , EIdentifier "x" ]
, ESymbol Rel "="
, EIdentifier "x"
]
]
, []
]
, [ [ EGrouped
[ EGrouped
[ EIdentifier "x" , ESymbol Bin "\9651" , EIdentifier "y" ]
, ESymbol Rel "="
, EGrouped
[ ESuper
(EIdentifier "h") (EGrouped [ ESymbol Bin "\8722" , ENumber "1" ])
, ESymbol Ord "\8290"
, EDelimited
"("
")"
[ Right
(EGrouped
[ EGrouped
[ EIdentifier "h"
, ESymbol Ord "\8289"
, EDelimited "(" ")" [ Right (EIdentifier "x") ]
]
, ESymbol Ord "\8290"
, EGrouped
[ EIdentifier "h"
, ESymbol Ord "\8289"
, EDelimited "(" ")" [ Right (EIdentifier "y") ]
]
])
]
]
]
]
, []
]
, [ [ EGrouped
[ EGrouped
[ EIdentifier "x" , ESymbol Bin "\9651" , EIdentifier "y" ]
, ESymbol Rel "="
, EGrouped
[ ESuper
(EIdentifier "f") (EGrouped [ ESymbol Bin "\8722" , ENumber "1" ])
, ESymbol Ord "\8290"
, EDelimited
"("
")"
[ Right
(EGrouped
[ EMathOperator "max"
, EDelimited
"{"
"}"
[ Right
(EGrouped
[ EGrouped
[ EGrouped
[ EIdentifier "f"
, ESymbol Ord "\8289"
, EDelimited "(" ")" [ Right (EIdentifier "x") ]
]
, ESymbol Bin "+"
, EGrouped
[ EIdentifier "f"
, ESymbol Ord "\8289"
, EDelimited "(" ")" [ Right (EIdentifier "y") ]
]
, ESymbol Bin "\8722"
, ENumber "1"
]
, ESymbol Pun ","
, ENumber "0"
])
]
])
]
]
]
]
, []
]
, [ [ EGrouped
[ EGrouped
[ EIdentifier "x" , ESymbol Bin "\9661" , EIdentifier "y" ]
, ESymbol Rel "="
, EGrouped
[ EIdentifier "\951"
, ESymbol Ord "\8289"
, EDelimited
"("
")"
[ Right
(EGrouped
[ EGrouped
[ EIdentifier "\951"
, ESymbol Ord "\8289"
, EDelimited "(" ")" [ Right (EIdentifier "x") ]
]
, ESymbol Bin "\9651"
, EGrouped
[ EIdentifier "\951"
, ESymbol Ord "\8289"
, EDelimited "(" ")" [ Right (EIdentifier "y") ]
]
])
]
]
]
]
, []
]
, [ [ EGrouped
[ EGrouped
[ EIdentifier "x"
, ESymbol Ord "\8290"
, EGrouped
[ ESub (ESymbol Bin "\9651") (ENumber "0") , EIdentifier "y" ]
]
, ESymbol Rel "="
, EDelimited
"{"
""
[ Right
(EArray
[ AlignCenter , AlignCenter , AlignCenter ]
[ [ [ EGrouped
[ EIdentifier "x" , ESymbol Bin "\8743" , EIdentifier "y" ]
]
, [ EText TextNormal "if" ]
, [ EGrouped
[ EIdentifier "x"
, ESymbol Bin "\8744"
, EGrouped [ EIdentifier "y" , ESymbol Rel "=" , ENumber "1" ]
]
]
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, [ [ ENumber "0" ]
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"\8971"
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NormalFrac
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NormalFrac
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NormalFrac
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NormalFrac
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NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
, Left "|"
, Right
(EUnderover False (ESymbol Op "\8721") (ENumber "1") (ENumber "2"))
]
]
, []
]
, [ [ EDelimited
"\8968"
"\8969"
[ Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
, Left "|"
, Right
(EUnderover False (ESymbol Op "\8721") (ENumber "1") (ENumber "2"))
]
]
, []
]
, [ [ EDelimited
""
""
[ Left "\8659"
, Right
(EDelimited
""
""
[ Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
, Left "\8597"
, Right
(EUnderover False (ESymbol Op "\8721") (ENumber "1") (ENumber "2"))
])
, Left "\8659"
]
]
, []
]
, [ [ EDelimited
"["
"]"
[ Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
]
]
, []
]
, [ [ EDelimited
"("
")"
[ Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
]
]
, []
]
, [ [ EDelimited
"{"
"}"
[ Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
]
]
, []
]
, [ [ EDelimited
"\9001"
"\9002"
[ Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
]
]
, []
]
, [ [ EDelimited
"\8970"
"\8971"
[ Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
]
]
, []
]
, [ [ EDelimited
"\8968"
"\8969"
[ Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
]
]
, []
]
, [ [ EDelimited
""
""
[ Left "\8593"
, Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
, Left "\8593"
]
]
, []
]
, [ [ EDelimited
""
""
[ Left "\8595"
, Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
, Left "\8595"
]
]
, []
]
, [ [ EDelimited
""
""
[ Left "\8597"
, Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
, Left "\8597"
]
]
, []
]
, [ [ EDelimited
""
""
[ Left "\8657"
, Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
, Left "\8657"
]
]
, []
]
, [ [ EDelimited
""
""
[ Left "\8659"
, Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
, Left "\8659"
]
]
, []
]
, [ [ EDelimited
""
""
[ Left "\8661"
, Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
, Left "\8661"
]
]
, []
]
, [ [ EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
]
, []
]
, [ [ EDelimited
"\\arrowvert"
"\\arrowvert"
[ Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
]
]
, []
]
, [ [ EDelimited
"\\Arrowvert"
"\\Arrowvert"
[ Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
]
]
, []
]
, [ [ EDelimited
"\\bracevert"
"\\bracevert"
[ Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
]
]
, []
]
, [ [ EDelimited
"|"
"|"
[ Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
]
]
, []
]
, [ [ EDelimited
"|"
"|"
[ Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
]
]
, []
]
, [ [ EDelimited
"|"
"|"
[ Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
]
]
, []
]
, [ [ EDelimited
""
""
[ Left "\8741"
, Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
, Left "\8741"
]
]
, []
]
, [ [ EDelimited
""
""
[ Left "\8741"
, Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
, Left "\8741"
]
]
, []
]
, [ [ EDelimited
""
""
[ Left "/"
, Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
, Left "/"
]
]
, []
]
, [ [ EDelimited
""
""
[ Left "\\"
, Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
, Left "\\"
]
]
, []
]
, [ [ EDelimited
"\9137"
"\9136"
[ Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
]
]
, []
]
, [ [ EDelimited
"\\lgroup"
"\\rgroup"
[ Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
]
]
, []
]
, [ [ EDelimited
"\8990"
"\8991"
[ Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
]
]
, []
]
, [ [ EDelimited
"\8988"
"\8989"
[ Right
(EFraction
NormalFrac
(EFraction NormalFrac (ENumber "1") (ENumber "2"))
(EFraction NormalFrac (ENumber "1") (ENumber "2")))
]
]
, []
]
, [ [ EGrouped
[ EIdentifier "A"
, EUnderover
False
(ESymbol Accent "\8592")
(ESpace (1 % 18))
(EGrouped
[ EIdentifier "n"
, ESymbol Bin "+"
, EIdentifier "\956"
, ESymbol Bin "\8722"
, ENumber "1"
])
, EIdentifier "B"
, EUnderover
False
(ESymbol Accent "\8594")
(EIdentifier "T")
(EGrouped
[ EIdentifier "n"
, ESymbol Bin "\177"
, EIdentifier "i"
, ESymbol Bin "\8722"
, ENumber "1"
])
, EIdentifier "C"
]
]
, []
]
, [ [ EFraction
NormalFrac
(ENumber "1")
(EGrouped
[ ESqrt (ENumber "2")
, ESymbol Bin "+"
, EFraction
NormalFrac
(ENumber "1")
(EGrouped
[ ESqrt (ENumber "3")
, ESymbol Bin "+"
, EFraction
NormalFrac
(ENumber "1")
(EGrouped
[ ESqrt (ENumber "4")
, ESymbol Bin "+"
, EFraction
NormalFrac
(ENumber "1")
(EGrouped
[ ESqrt (ENumber "5")
, ESymbol Bin "+"
, EFraction
NormalFrac
(ENumber "1")
(EGrouped
[ ESqrt (ENumber "6")
, ESymbol Bin "+"
, EIdentifier "\8230"
])
])
])
])
])
]
, []
]
, [ [ EFraction
NormalFrac
(ENumber "1")
(EGrouped
[ ESqrt (ENumber "2")
, ESymbol Bin "+"
, EFraction
NormalFrac
(ENumber "1")
(EGrouped
[ ESqrt (ENumber "3")
, ESymbol Bin "+"
, EFraction
NormalFrac
(ENumber "1")
(EGrouped
[ ESqrt (ENumber "4")
, ESymbol Bin "+"
, EFraction
NormalFrac
(ENumber "1")
(EGrouped
[ ESqrt (ENumber "5")
, ESymbol Bin "+"
, EFraction
NormalFrac
(ENumber "1")
(EGrouped
[ ESqrt (ENumber "6")
, ESymbol Bin "+"
, EIdentifier "\8230"
])
])
])
])
])
]
, []
]
, [ [ EDelimited
"("
"\8971"
[ Right
(EFraction
NormalFrac
(EGrouped
[ EMathOperator "sin" , ESymbol Ord "\8289" , EIdentifier "\952" ])
(EIdentifier "M"))
]
]
, []
]
, [ [ EDelimited
"("
"\8971"
[ Right
(EFraction
NormalFrac
(EGrouped
[ EMathOperator "sin" , ESymbol Ord "\8289" , EIdentifier "\952" ])
(EIdentifier "M"))
]
]
, []
]
, [ [ EDelimited
"("
"\8971"
[ Right
(EFraction
NormalFrac
(EGrouped
[ EMathOperator "sin" , ESymbol Ord "\8289" , EIdentifier "\952" ])
(EIdentifier "M"))
]
]
, []
]
, [ [ EDelimited
"("
"\8971"
[ Right
(EFraction
NormalFrac
(EGrouped
[ EMathOperator "sin" , ESymbol Ord "\8289" , EIdentifier "\952" ])
(EIdentifier "M"))
]
]
, []
]
, [ [ EDelimited
"("
"\8971"
[ Right
(EFraction
NormalFrac
(EGrouped
[ EMathOperator "sin" , ESymbol Ord "\8289" , EIdentifier "\952" ])
(EIdentifier "M"))
]
]
, []
]
, [ [ EDelimited
"("
"\8971"
[ Right
(EFraction
NormalFrac
(EGrouped
[ EMathOperator "sin" , ESymbol Ord "\8289" , EIdentifier "\952" ])
(EIdentifier "M"))
]
]
, []
]
, [ [ EDelimited
"("
"\8971"
[ Right
(EFraction
NormalFrac
(EGrouped
[ EMathOperator "sin" , ESymbol Ord "\8289" , EIdentifier "\952" ])
(EIdentifier "M"))
]
]
, []
]
, [ [ EDelimited
"("
"\8971"
[ Right
(EFraction
NormalFrac
(EGrouped
[ EMathOperator "sin" , ESymbol Ord "\8289" , EIdentifier "\952" ])
(EIdentifier "M"))
]
]
, []
]
, [ [ EDelimited
"("
"\8971"
[ Right
(EFraction
NormalFrac
(EGrouped
[ EMathOperator "sin" , ESymbol Ord "\8289" , EIdentifier "\952" ])
(EIdentifier "M"))
]
]
, []
]
, [ [ EFraction
NormalFrac
(EGrouped
[ EMathOperator "sin" , ESymbol Ord "\8289" , EIdentifier "\952" ])
(EIdentifier "M")
]
, []
]
, [ [ EFraction
NormalFrac
(EGrouped
[ EMathOperator "sin" , ESymbol Ord "\8289" , EIdentifier "\952" ])
(EIdentifier "M")
]
, []
]
, [ [ EFraction
NormalFrac
(EGrouped
[ EMathOperator "sin" , ESymbol Ord "\8289" , EIdentifier "\952" ])
(EIdentifier "M")
]
, []
]
, [ [ EFraction
NormalFrac
(EGrouped
[ EMathOperator "sin" , ESymbol Ord "\8289" , EIdentifier "\952" ])
(EIdentifier "M")
]
, []
]
, [ [ EFraction
NormalFrac
(EGrouped
[ EMathOperator "sin" , ESymbol Ord "\8289" , EIdentifier "\952" ])
(EIdentifier "M")
]
, []
]
, [ [ EFraction
NormalFrac
(EGrouped
[ EMathOperator "sin" , ESymbol Ord "\8289" , EIdentifier "\952" ])
(EIdentifier "M")
]
, []
]
, [ [ EFraction
NormalFrac
(EGrouped
[ EMathOperator "sin" , ESymbol Ord "\8289" , EIdentifier "\952" ])
(EIdentifier "M")
]
, []
]
, [ [ EFraction
NormalFrac
(EGrouped
[ EMathOperator "sin" , ESymbol Ord "\8289" , EIdentifier "\952" ])
(EIdentifier "M")
]
, []
]
, [ [ EFraction
NormalFrac
(EGrouped
[ EMathOperator "sin" , ESymbol Ord "\8289" , EIdentifier "\952" ])
(EIdentifier "M")
]
, []
]
]
]
>>> omml
<?xml version='1.0' ?>
<m:oMathPara>
<m:oMathParaPr>
<m:jc m:val="center" />
</m:oMathParaPr>
<m:oMath>
<m:m>
<m:mPr>
<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:r>
<m:t>2</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁢</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∑</m:t>
</m:r>
<m:r>
<m:t>a</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁢</m:t>
</m:r>
<m:r>
<m:t>b</m:t>
</m:r>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:sSup>
<m:e>
<m:r>
<m:t>x</m:t>
</m:r>
</m:e>
<m:sup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>′</m:t>
</m:r>
<m:r>
<m:t>3</m:t>
</m:r>
</m:sup>
</m:sSup>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:sSup>
<m:e>
<m:r>
<m:t>f</m:t>
</m:r>
</m:e>
<m:sup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>′</m:t>
</m:r>
</m:sup>
</m:sSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>(</m:t>
</m:r>
<m:r>
<m:t>x</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>)</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>cos</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>f</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>(</m:t>
</m:r>
<m:r>
<m:t>z</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>)</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:nary>
<m:naryPr>
<m:chr m:val="∑" />
<m:limLoc m:val="undOvr" />
<m:subHide m:val="0" />
<m:supHide m:val="0" />
</m:naryPr>
<m:sub>
<m:r>
<m:t>n</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:r>
<m:t>0</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>∞</m:t>
</m:r>
</m:sup>
<m:e>
<m:sSub>
<m:e>
<m:r>
<m:t>a</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>n</m:t>
</m:r>
</m:sub>
</m:sSub>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁢</m:t>
</m:r>
<m:sSup>
<m:e>
<m:r>
<m:t>z</m:t>
</m:r>
</m:e>
<m:sup>
<m:r>
<m:t>n</m:t>
</m:r>
</m:sup>
</m:sSup>
</m:e>
</m:nary>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>, </m:t>
</m:r>
<m:d>
<m:dPr>
<m:begChr m:val="|" />
<m:endChr m:val="|" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:r>
<m:t>z</m:t>
</m:r>
</m:e>
</m:d>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t><</m:t>
</m:r>
<m:r>
<m:t>R</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>​</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>(</m:t>
</m:r>
<m:r>
<m:t>R</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>≠</m:t>
</m:r>
<m:r>
<m:t>0</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>)</m:t>
</m:r>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="∫" />
<m:endChr m:val="" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:sSub>
<m:e>
<m:r>
<m:t>​</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>C</m:t>
</m:r>
</m:sub>
</m:sSub>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val=")" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:nary>
<m:naryPr>
<m:chr m:val="∑" />
<m:limLoc m:val="undOvr" />
<m:subHide m:val="0" />
<m:supHide m:val="0" />
</m:naryPr>
<m:sub>
<m:r>
<m:t>n</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:r>
<m:t>0</m:t>
</m:r>
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<m:t> μF</m:t>
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<m:t>−</m:t>
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<m:t> μS</m:t>
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<m:t> μV</m:t>
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<m:t> GΩ</m:t>
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<m:t> kΩ</m:t>
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<m:t>−</m:t>
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<m:t> MΩ</m:t>
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<m:t>+</m:t>
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<m:t> mΩ</m:t>
</m:r>
<m:r>
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<m:t>−</m:t>
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<m:r>
<m:t>10</m:t>
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<m:t> Ω</m:t>
</m:r>
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<m:t> Btu</m:t>
</m:r>
<m:r>
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<m:t>+</m:t>
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<m:t> cal</m:t>
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<m:t>−</m:t>
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<m:t> eV</m:t>
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<m:r>
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<m:t> erg</m:t>
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<m:r>
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<m:t>−</m:t>
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<m:r>
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<m:t> GeV</m:t>
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<m:t>+</m:t>
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<m:t> GJ</m:t>
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</m:e>
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<m:t> J</m:t>
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<m:t>+</m:t>
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<m:t> kcal</m:t>
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<m:t>−</m:t>
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<m:t> MeV</m:t>
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<m:t> MJ</m:t>
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<m:t> μJ</m:t>
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<m:r>
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<m:t>−</m:t>
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<m:t> mJ</m:t>
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<m:t>+</m:t>
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<m:t> nJ</m:t>
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<m:t> dyn</m:t>
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<m:t> kN</m:t>
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<m:r>
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<m:t>−</m:t>
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<m:r>
<m:t>10</m:t>
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<m:r>
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<m:t> MN</m:t>
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<m:r>
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<m:t>+</m:t>
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<m:r>
<m:t>10</m:t>
</m:r>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t> μN</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>−</m:t>
</m:r>
<m:r>
<m:t>10</m:t>
</m:r>
<m:r>
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<m:nor />
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<m:t> mN</m:t>
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<m:r>
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<m:sty m:val="p" />
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<m:t>+</m:t>
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<m:r>
<m:t>10</m:t>
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<m:t> N</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>−</m:t>
</m:r>
<m:r>
<m:t>10</m:t>
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<m:r>
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<m:t> ozf</m:t>
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<m:r>
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<m:t>+</m:t>
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<m:r>
<m:t>10</m:t>
</m:r>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
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<m:t> lbf</m:t>
</m:r>
</m:e>
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<m:mr>
<m:e>
<m:r>
<m:t>10</m:t>
</m:r>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t> EHz</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>+</m:t>
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<m:r>
<m:t>10</m:t>
</m:r>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t> GHz</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>−</m:t>
</m:r>
<m:r>
<m:t>10</m:t>
</m:r>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t> Hz</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:r>
<m:t>10</m:t>
</m:r>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t> kHz</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>−</m:t>
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<m:r>
<m:t>10</m:t>
</m:r>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t> MHz</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>+</m:t>
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<m:r>
<m:t>10</m:t>
</m:r>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t> PHz</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>−</m:t>
</m:r>
<m:r>
<m:t>10</m:t>
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<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t> THz</m:t>
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</m:e>
<m:e />
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<m:mr>
<m:e>
<m:r>
<m:t>10</m:t>
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<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
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<m:t> fc</m:t>
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<m:sty m:val="p" />
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<m:t>+</m:t>
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<m:t>10</m:t>
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<m:t> lx</m:t>
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<m:r>
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<m:r>
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<m:t>2</m:t>
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<m:e />
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<m:mr>
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<m:t>2</m:t>
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<m:r>
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<m:t>2</m:t>
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<m:r>
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<m:t>1</m:t>
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<m:t>2</m:t>
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<m:e />
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<m:mr>
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<m:t>1</m:t>
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<m:t>2</m:t>
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<m:r>
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<m:t>2</m:t>
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<m:r>
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<m:mr>
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<m:r>
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<m:r>
<m:t>a</m:t>
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<m:r>
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</m:r>
<m:r>
<m:t>b</m:t>
</m:r>
<m:r>
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<m:r>
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<m:t>=</m:t>
</m:r>
<m:r>
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<m:r>
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<m:r>
<m:t>a</m:t>
</m:r>
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<m:r>
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<m:r>
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<m:t>2</m:t>
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<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⋅</m:t>
</m:r>
<m:r>
<m:t>7</m:t>
</m:r>
<m:r>
<m:rPr>
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<m:t>+</m:t>
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<m:r>
<m:t>3</m:t>
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<m:r>
<m:rPr>
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<m:r>
<m:t>5</m:t>
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<m:den>
<m:r>
<m:t>35</m:t>
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<m:r>
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</m:r>
<m:f>
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<m:num>
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<m:r>
<m:t>35</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
<m:e />
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<m:mr>
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<m:r>
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<m:mr>
<m:e>
<m:r>
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<m:e>
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<m:e>
<m:r>
<m:t>a</m:t>
</m:r>
<m:r>
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<m:r>
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<m:mr>
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<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:r>
<m:t>a</m:t>
</m:r>
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<m:e>
<m:r>
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<m:e>
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<m:r>
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<m:sty m:val="p" />
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<m:r>
<m:t>0</m:t>
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</m:m>
</m:e>
</m:d>
</m:e>
<m:e />
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<m:mr>
<m:e>
<m:sSup>
<m:e>
<m:r>
<m:t>a</m:t>
</m:r>
</m:e>
<m:sup>
<m:r>
<m:t>n</m:t>
</m:r>
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<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>=</m:t>
</m:r>
<m:limLow>
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<m:limLow>
<m:e>
<m:r>
<m:t>a</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⋅</m:t>
</m:r>
<m:r>
<m:t>a</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⋅</m:t>
</m:r>
<m:r>
<m:t>⋯</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⋅</m:t>
</m:r>
<m:r>
<m:t>a</m:t>
</m:r>
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<m:lim>
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<m:rPr>
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<m:t>︸</m:t>
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<m:lim>
<m:r>
<m:t>n</m:t>
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<m:r>
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<m:t> factors</m:t>
</m:r>
</m:lim>
</m:limLow>
</m:e>
<m:e />
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<m:mr>
<m:e>
<m:sSup>
<m:e>
<m:d>
<m:dPr>
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<m:e>
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<m:num>
<m:r>
<m:t>a</m:t>
</m:r>
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<m:den>
<m:r>
<m:t>b</m:t>
</m:r>
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</m:e>
</m:d>
</m:e>
<m:sup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>−</m:t>
</m:r>
<m:r>
<m:t>n</m:t>
</m:r>
</m:sup>
</m:sSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>=</m:t>
</m:r>
<m:sSup>
<m:e>
<m:d>
<m:dPr>
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<m:e>
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<m:fPr>
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<m:num>
<m:r>
<m:t>b</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>a</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
</m:d>
</m:e>
<m:sup>
<m:r>
<m:t>n</m:t>
</m:r>
</m:sup>
</m:sSup>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:rad>
<m:deg>
<m:r>
<m:t>n</m:t>
</m:r>
</m:deg>
<m:e>
<m:r>
<m:t>a</m:t>
</m:r>
</m:e>
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<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>=</m:t>
</m:r>
<m:r>
<m:t>b</m:t>
</m:r>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t> means </m:t>
</m:r>
<m:sSup>
<m:e>
<m:r>
<m:t>b</m:t>
</m:r>
</m:e>
<m:sup>
<m:r>
<m:t>n</m:t>
</m:r>
</m:sup>
</m:sSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:r>
<m:t>a</m:t>
</m:r>
<m:r>
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<m:r>
<m:t>1</m:t>
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<m:r>
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<m:r>
<m:t>123</m:t>
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<m:e>
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<m:baseJc m:val="center" />
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<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
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</m:mc>
<m:mc>
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<m:mcJc m:val="center" />
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</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
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</m:mc>
<m:mc>
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<m:mcJc m:val="center" />
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</m:mcs>
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<m:mr>
<m:e>
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<m:t>t</m:t>
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</m:e>
<m:e>
<m:r>
<m:t>x</m:t>
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</m:e>
<m:e>
<m:r>
<m:t>y</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>z</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>1.0000</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>1.0000</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>1.0000</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>.1</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>1.1158</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>1.0938</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>.8842</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>.2</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>1.2668</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>1.1695</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>.7332</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>.3</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>1.4582</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>1.2173</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>.5418</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>.4</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>1.6953</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>1.2253</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>.3047</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>.5</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>1.9830</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>1.1791</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>.0170</m:t>
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</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>.6</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>2.3256</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>1.0619</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>−</m:t>
</m:r>
<m:r>
<m:t>.3256</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>.7</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>2.7265</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>.8542</m:t>
</m:r>
</m:e>
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<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>−</m:t>
</m:r>
<m:r>
<m:t>.7265</m:t>
</m:r>
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</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>.8</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>3.1873</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>.5344</m:t>
</m:r>
</m:e>
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<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>−</m:t>
</m:r>
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<m:t>1.1873</m:t>
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</m:dPr>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>arccos</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>7</m:t>
</m:r>
</m:den>
</m:f>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁢</m:t>
</m:r>
<m:rad>
<m:radPr>
<m:degHide m:val="1" />
</m:radPr>
<m:deg />
<m:e>
<m:r>
<m:t>14</m:t>
</m:r>
</m:e>
</m:rad>
</m:e>
</m:d>
</m:e>
<m:e>
<m:sSub>
<m:e>
<m:r>
<m:t>X</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>3</m:t>
</m:r>
</m:sub>
</m:sSub>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∈</m:t>
</m:r>
<m:r>
<m:t>ℤ</m:t>
</m:r>
</m:e>
</m:d>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>,</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∈</m:t>
</m:r>
<m:d>
<m:dPr>
<m:begChr m:val="{" />
<m:endChr m:val="}" />
<m:sepChr m:val="|" />
<m:grow />
</m:dPr>
<m:e>
<m:r>
<m:t>2</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⁢</m:t>
</m:r>
<m:sSub>
<m:e>
<m:r>
<m:t>X</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>4</m:t>
</m:r>
</m:sub>
</m:sSub>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⁢</m:t>
</m:r>
<m:r>
<m:t>π</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>−</m:t>
</m:r>
<m:r>
<m:t>π</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>+</m:t>
</m:r>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val=")" />
<m:sepChr m:val="" />
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</m:dPr>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>arccos</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⁡</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>7</m:t>
</m:r>
</m:den>
</m:f>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⁢</m:t>
</m:r>
<m:rad>
<m:radPr>
<m:degHide m:val="1" />
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<m:deg />
<m:e>
<m:r>
<m:t>14</m:t>
</m:r>
</m:e>
</m:rad>
</m:e>
</m:d>
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<m:e>
<m:sSub>
<m:e>
<m:r>
<m:t>X</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>4</m:t>
</m:r>
</m:sub>
</m:sSub>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∈</m:t>
</m:r>
<m:r>
<m:t>ℤ</m:t>
</m:r>
</m:e>
</m:d>
</m:e>
<m:e />
</m:mr>
<m:mr>
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<m:t>P</m:t>
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<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:r>
<m:t>A</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⁢</m:t>
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<m:sSup>
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<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val=")" />
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</m:dPr>
<m:e>
<m:sSup>
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<m:r>
<m:t>A</m:t>
</m:r>
</m:e>
<m:sup>
<m:r>
<m:t>T</m:t>
</m:r>
</m:sup>
</m:sSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⁢</m:t>
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<m:r>
<m:t>A</m:t>
</m:r>
</m:e>
</m:d>
</m:e>
<m:sup>
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<m:sty m:val="p" />
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<m:t>−</m:t>
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<m:r>
<m:t>1</m:t>
</m:r>
</m:sup>
</m:sSup>
<m:r>
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<m:sty m:val="p" />
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<m:t>⁢</m:t>
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<m:t>A</m:t>
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<m:sup>
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<m:t>T</m:t>
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</m:e>
<m:e />
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<m:sty m:val="p" />
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<m:t>det</m:t>
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<m:d>
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<m:begChr m:val="(" />
<m:endChr m:val=")" />
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</m:dPr>
<m:e>
<m:m>
<m:mPr>
<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
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</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
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</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
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</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
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<m:t>x</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>y</m:t>
</m:r>
</m:e>
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<m:r>
<m:t>1</m:t>
</m:r>
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<m:mr>
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<m:t>a</m:t>
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<m:e>
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<m:t>b</m:t>
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<m:t>1</m:t>
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<m:t>a</m:t>
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<m:e>
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<m:t>d</m:t>
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<m:t>1</m:t>
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</m:m>
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<m:t>x</m:t>
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<m:t>⁢</m:t>
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<m:t>b</m:t>
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<m:t>−</m:t>
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<m:t>x</m:t>
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<m:t>d</m:t>
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<m:sty m:val="p" />
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<m:t>+</m:t>
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<m:t>a</m:t>
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<m:t>d</m:t>
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<m:sty m:val="p" />
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<m:t>b</m:t>
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<m:t>A</m:t>
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<m:sty m:val="p" />
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<m:t>⁡</m:t>
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<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val=")" />
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<m:grow />
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<m:e>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:e>
</m:d>
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<m:rPr>
<m:sty m:val="p" />
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<m:t>⁢</m:t>
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<m:r>
<m:t>A</m:t>
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<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⁡</m:t>
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<m:d>
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<m:begChr m:val="(" />
<m:endChr m:val=")" />
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</m:dPr>
<m:e>
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<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>−</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:e>
</m:d>
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<m:t>=</m:t>
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<m:mcJc m:val="center" />
<m:count m:val="1" />
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</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
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</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>cos</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:e>
<m:e>
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<m:rPr>
<m:sty m:val="p" />
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<m:t>−</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:rPr>
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</m:rPr>
<m:t>cos</m:t>
</m:r>
<m:r>
<m:rPr>
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<m:t>⁡</m:t>
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<m:r>
<m:t>θ</m:t>
</m:r>
</m:e>
</m:mr>
</m:m>
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<m:t>⁢</m:t>
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<m:d>
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</m:dPr>
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<m:count m:val="1" />
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<m:mcPr>
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<m:count m:val="1" />
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</m:mPr>
<m:mr>
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</m:rPr>
<m:t>cos</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⁡</m:t>
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<m:r>
<m:t>θ</m:t>
</m:r>
</m:e>
<m:e>
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<m:rPr>
<m:sty m:val="p" />
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<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
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<m:sty m:val="p" />
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<m:t>−</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>cos</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:e>
</m:mr>
</m:m>
</m:e>
</m:d>
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<m:e />
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<m:t>J</m:t>
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<m:t>⁡</m:t>
</m:r>
<m:r>
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<m:t>(</m:t>
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<m:r>
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<m:sty m:val="p" />
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<m:t>)</m:t>
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<m:r>
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<m:t>=</m:t>
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<m:d>
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<m:e>
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<m:mPr>
<m:baseJc m:val="center" />
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<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
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</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
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</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
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</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
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</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
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<m:r>
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</m:e>
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<m:t>n</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>1</m:t>
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</m:sub>
</m:sSub>
</m:sub>
</m:sSub>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⁡</m:t>
</m:r>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val=")" />
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</m:dPr>
<m:e>
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<m:e>
<m:r>
<m:t>λ</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sub>
</m:sSub>
</m:e>
</m:d>
</m:e>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>⋯</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
<m:e>
<m:sSub>
<m:e>
<m:r>
<m:t>J</m:t>
</m:r>
</m:e>
<m:sub>
<m:sSub>
<m:e>
<m:r>
<m:t>n</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sub>
</m:sSub>
</m:sub>
</m:sSub>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val=")" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:sSub>
<m:e>
<m:r>
<m:t>λ</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sub>
</m:sSub>
</m:e>
</m:d>
</m:e>
<m:e>
<m:r>
<m:t>⋯</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>⋮</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>⋮</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>⋱</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>⋮</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>⋯</m:t>
</m:r>
</m:e>
<m:e>
<m:sSub>
<m:e>
<m:r>
<m:t>J</m:t>
</m:r>
</m:e>
<m:sub>
<m:sSub>
<m:e>
<m:r>
<m:t>n</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>k</m:t>
</m:r>
</m:sub>
</m:sSub>
</m:sub>
</m:sSub>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val=")" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:sSub>
<m:e>
<m:r>
<m:t>λ</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>k</m:t>
</m:r>
</m:sub>
</m:sSub>
</m:e>
</m:d>
</m:e>
</m:mr>
</m:m>
</m:e>
</m:d>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>det</m:t>
</m:r>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val=")" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:m>
<m:mPr>
<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>−</m:t>
</m:r>
<m:r>
<m:t>4</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:r>
<m:t>X</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>−</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>−</m:t>
</m:r>
<m:r>
<m:t>4</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:r>
<m:t>X</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>−</m:t>
</m:r>
<m:r>
<m:t>4</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:r>
<m:t>X</m:t>
</m:r>
</m:e>
</m:mr>
</m:m>
</m:e>
</m:d>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:sSup>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val=")" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:r>
<m:t>X</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>−</m:t>
</m:r>
<m:r>
<m:t>4</m:t>
</m:r>
</m:e>
</m:d>
</m:e>
<m:sup>
<m:r>
<m:t>3</m:t>
</m:r>
</m:sup>
</m:sSup>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="" />
<m:endChr m:val="" />
<m:sepChr m:val="↔" />
<m:grow />
</m:dPr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="{" />
<m:endChr m:val="}" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val=")" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:m>
<m:mPr>
<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>−</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>2</m:t>
</m:r>
</m:den>
</m:f>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>−</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>6</m:t>
</m:r>
</m:den>
</m:f>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁢</m:t>
</m:r>
<m:rad>
<m:radPr>
<m:degHide m:val="1" />
</m:radPr>
<m:deg />
<m:e>
<m:r>
<m:t>33</m:t>
</m:r>
</m:e>
</m:rad>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>1</m:t>
</m:r>
</m:e>
</m:mr>
</m:m>
</m:e>
</m:d>
</m:e>
</m:d>
</m:e>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>5</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>2</m:t>
</m:r>
</m:den>
</m:f>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>−</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>2</m:t>
</m:r>
</m:den>
</m:f>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁢</m:t>
</m:r>
<m:rad>
<m:radPr>
<m:degHide m:val="1" />
</m:radPr>
<m:deg />
<m:e>
<m:r>
<m:t>33</m:t>
</m:r>
</m:e>
</m:rad>
</m:e>
</m:d>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="" />
<m:endChr m:val="" />
<m:sepChr m:val="∥" />
<m:grow />
</m:dPr>
<m:e />
<m:e>
<m:r>
<m:t>A</m:t>
</m:r>
</m:e>
<m:e />
</m:d>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:limLow>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>max</m:t>
</m:r>
</m:e>
<m:lim>
<m:r>
<m:t>x</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>≠</m:t>
</m:r>
<m:r>
<m:t>0</m:t>
</m:r>
</m:lim>
</m:limLow>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:d>
<m:dPr>
<m:begChr m:val="" />
<m:endChr m:val="" />
<m:sepChr m:val="∥" />
<m:grow />
</m:dPr>
<m:e />
<m:e>
<m:r>
<m:t>A</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁢</m:t>
</m:r>
<m:r>
<m:t>x</m:t>
</m:r>
</m:e>
<m:e />
</m:d>
</m:num>
<m:den>
<m:d>
<m:dPr>
<m:begChr m:val="" />
<m:endChr m:val="" />
<m:sepChr m:val="∥" />
<m:grow />
</m:dPr>
<m:e />
<m:e>
<m:r>
<m:t>x</m:t>
</m:r>
</m:e>
<m:e />
</m:d>
</m:den>
</m:f>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val=")" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:m>
<m:mPr>
<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:sSub>
<m:e>
<m:r>
<m:t>a</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>1</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>​</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sub>
</m:sSub>
</m:e>
<m:e>
<m:sSub>
<m:e>
<m:r>
<m:t>a</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>1</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>​</m:t>
</m:r>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sub>
</m:sSub>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:sSub>
<m:e>
<m:r>
<m:t>a</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>2</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>​</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sub>
</m:sSub>
</m:e>
<m:e>
<m:sSub>
<m:e>
<m:r>
<m:t>a</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>2</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>​</m:t>
</m:r>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sub>
</m:sSub>
</m:e>
</m:mr>
</m:m>
</m:e>
</m:d>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val=")" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:m>
<m:mPr>
<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:sSub>
<m:e>
<m:r>
<m:t>b</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>1</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>​</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sub>
</m:sSub>
</m:e>
<m:e>
<m:sSub>
<m:e>
<m:r>
<m:t>b</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>1</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>​</m:t>
</m:r>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sub>
</m:sSub>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:sSub>
<m:e>
<m:r>
<m:t>b</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>2</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>​</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sub>
</m:sSub>
</m:e>
<m:e>
<m:sSub>
<m:e>
<m:r>
<m:t>b</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>2</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>​</m:t>
</m:r>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sub>
</m:sSub>
</m:e>
</m:mr>
</m:m>
</m:e>
</m:d>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val=")" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:m>
<m:mPr>
<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:sSub>
<m:e>
<m:r>
<m:t>a</m:t>
</m:r>
</m:e>
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<m:t>2</m:t>
</m:r>
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<m:sty m:val="p" />
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<m:t>1</m:t>
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<m:t>2</m:t>
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<m:sty m:val="p" />
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<m:t>⁡</m:t>
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<m:sty m:val="p" />
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<m:mcJc m:val="center" />
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<m:t>3</m:t>
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</m:mr>
</m:m>
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</m:d>
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<m:t>2</m:t>
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<m:sty m:val="p" />
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<m:t>−</m:t>
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<m:r>
<m:t>5</m:t>
</m:r>
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<m:sty m:val="p" />
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<m:t>⁢</m:t>
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<m:d>
<m:dPr>
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<m:mcs>
<m:mc>
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<m:mcJc m:val="center" />
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<m:mc>
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<m:sty m:val="p" />
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<m:sty m:val="p" />
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<m:t>0</m:t>
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<m:sty m:val="p" />
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<m:t>=</m:t>
</m:r>
<m:limLow>
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<m:rPr>
<m:sty m:val="p" />
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<m:t>lim</m:t>
</m:r>
</m:e>
<m:lim>
<m:r>
<m:t>x</m:t>
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<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
</m:lim>
</m:limLow>
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<m:sub>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>2</m:t>
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</m:sup>
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</m:nary>
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<m:naryPr>
<m:chr m:val="∫" />
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<m:supHide m:val="0" />
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<m:sub>
<m:r>
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</m:r>
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<m:rPr>
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<m:r>
<m:t>x</m:t>
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</m:e>
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<m:limLow>
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<m:sty m:val="p" />
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<m:t>lim</m:t>
</m:r>
</m:e>
<m:lim>
<m:r>
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<m:sty m:val="p" />
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<m:t>∥</m:t>
</m:r>
<m:r>
<m:t>P</m:t>
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<m:r>
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<m:sty m:val="p" />
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<m:t>∥</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>→</m:t>
</m:r>
<m:r>
<m:t>0</m:t>
</m:r>
</m:lim>
</m:limLow>
<m:nary>
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<m:t>i</m:t>
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<m:r>
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<m:sty m:val="p" />
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<m:t>=</m:t>
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<m:r>
<m:t>1</m:t>
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<m:sup>
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<m:t>n</m:t>
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</m:sup>
<m:e>
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<m:r>
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<m:sty m:val="p" />
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</m:r>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val=")" />
<m:sepChr m:val="" />
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<m:e>
<m:sSub>
<m:e>
<m:acc>
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<m:e>
<m:r>
<m:t>x</m:t>
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</m:e>
</m:acc>
</m:e>
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</m:sub>
</m:sSub>
</m:e>
</m:d>
<m:r>
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<m:sty m:val="p" />
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<m:t>⁢</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>Δ</m:t>
</m:r>
<m:sSub>
<m:e>
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<m:t>x</m:t>
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</m:e>
<m:sub>
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</m:e>
</m:nary>
</m:e>
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<m:mr>
<m:e>
<m:nary>
<m:naryPr>
<m:chr m:val="∫" />
<m:limLoc m:val="subSup" />
<m:subHide m:val="0" />
<m:supHide m:val="0" />
</m:naryPr>
<m:sub>
<m:r>
<m:t>a</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>b</m:t>
</m:r>
</m:sup>
<m:e>
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<m:t>f</m:t>
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<m:sty m:val="p" />
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<m:t>⁡</m:t>
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<m:r>
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<m:sty m:val="p" />
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<m:t>)</m:t>
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<m:t>⁢</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:r>
<m:t>x</m:t>
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</m:e>
</m:nary>
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<m:sty m:val="p" />
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<m:t>lim</m:t>
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<m:t>n</m:t>
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<m:r>
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<m:t>→</m:t>
</m:r>
<m:r>
<m:t>∞</m:t>
</m:r>
</m:lim>
</m:limLow>
<m:f>
<m:fPr>
<m:type m:val="bar" />
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<m:num>
<m:r>
<m:t>b</m:t>
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<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>−</m:t>
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<m:r>
<m:t>a</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>n</m:t>
</m:r>
</m:den>
</m:f>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁢</m:t>
</m:r>
<m:nary>
<m:naryPr>
<m:chr m:val="∑" />
<m:limLoc m:val="undOvr" />
<m:subHide m:val="0" />
<m:supHide m:val="0" />
</m:naryPr>
<m:sub>
<m:r>
<m:t>i</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
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<m:r>
<m:t>1</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>n</m:t>
</m:r>
</m:sup>
<m:e>
<m:r>
<m:t>f</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
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<m:t>testing </m:t>
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<m:t> end.</m:t>
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<m:num>
<m:r>
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<m:t>ⅆ</m:t>
</m:r>
<m:r>
<m:t>f</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>ⅆ</m:t>
</m:r>
<m:r>
<m:t>x</m:t>
</m:r>
</m:den>
</m:f>
<m:r>
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<m:sty m:val="p" />
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<m:t>⁡</m:t>
</m:r>
<m:r>
<m:rPr>
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<m:t>(</m:t>
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<m:t>)</m:t>
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<m:t>=</m:t>
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<m:r>
<m:t>5</m:t>
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<m:mr>
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<m:rPr>
<m:sty m:val="p" />
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<m:t>∫</m:t>
</m:r>
<m:r>
<m:t>x</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⁢</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>ⅆ</m:t>
</m:r>
<m:r>
<m:t>x</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∬</m:t>
</m:r>
<m:r>
<m:t>x</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁢</m:t>
</m:r>
<m:r>
<m:t>y</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁢</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>ⅆ</m:t>
</m:r>
<m:r>
<m:t>x</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁢</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>ⅆ</m:t>
</m:r>
<m:r>
<m:t>y</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
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</m:r>
</m:e>
<m:sup>
<m:r>
<m:t>y</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>−</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sup>
</m:sSup>
</m:num>
<m:den>
<m:r>
<m:t>12.34</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
</m:rad>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t> </m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>1</m:t>
</m:r>
</m:e>
</m:mr>
</m:m>
</m:e>
</m:mr>
</m:m>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:m>
<m:mPr>
<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
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</m:mc>
<m:mc>
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<m:count m:val="1" />
</m:mcPr>
</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>1</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>1</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
</m:mr>
</m:m>
</m:e>
<m:e />
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<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
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<m:e>
<m:m>
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<m:baseJc m:val="center" />
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<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
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</m:mc>
<m:mc>
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<m:mcJc m:val="center" />
<m:count m:val="1" />
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</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>−</m:t>
</m:r>
<m:r>
<m:t>i</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>i</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
</m:mr>
</m:m>
</m:e>
</m:d>
</m:e>
<m:e />
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<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="[" />
<m:endChr m:val="]" />
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<m:grow />
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<m:e>
<m:m>
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<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
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</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:r>
<m:t>1</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>−</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
</m:e>
</m:mr>
</m:m>
</m:e>
</m:d>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="|" />
<m:endChr m:val="|" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:m>
<m:mPr>
<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
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</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
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</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:r>
<m:t>a</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>b</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>c</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>d</m:t>
</m:r>
</m:e>
</m:mr>
</m:m>
</m:e>
</m:d>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="" />
<m:endChr m:val="" />
<m:sepChr m:val="∥" />
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<m:e />
<m:e>
<m:m>
<m:mPr>
<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
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</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:r>
<m:t>1</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>1</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>11</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t> </m:t>
</m:r>
</m:e>
</m:mr>
</m:m>
</m:e>
<m:e />
</m:d>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:m>
<m:mPr>
<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:r>
<m:t>1</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>2</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>3</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>4</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>5</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t> </m:t>
</m:r>
</m:e>
</m:mr>
</m:m>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>testing </m:t>
</m:r>
<m:m>
<m:mPr>
<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:e>
</m:mr>
</m:m>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:acc>
<m:accPr>
<m:chr m:val="̂" />
</m:accPr>
<m:e>
<m:r>
<m:t>a</m:t>
</m:r>
</m:e>
</m:acc>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:acc>
<m:accPr>
<m:chr m:val="ˇ" />
</m:accPr>
<m:e>
<m:r>
<m:t>b</m:t>
</m:r>
</m:e>
</m:acc>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:acc>
<m:accPr>
<m:chr m:val="˜" />
</m:accPr>
<m:e>
<m:r>
<m:t>c</m:t>
</m:r>
</m:e>
</m:acc>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:acc>
<m:accPr>
<m:chr m:val="´" />
</m:accPr>
<m:e>
<m:r>
<m:t>d</m:t>
</m:r>
</m:e>
</m:acc>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:acc>
<m:accPr>
<m:chr m:val="`" />
</m:accPr>
<m:e>
<m:r>
<m:t>e</m:t>
</m:r>
</m:e>
</m:acc>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:acc>
<m:accPr>
<m:chr m:val="˘" />
</m:accPr>
<m:e>
<m:r>
<m:t>f</m:t>
</m:r>
</m:e>
</m:acc>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:acc>
<m:accPr>
<m:chr m:val="¯" />
</m:accPr>
<m:e>
<m:r>
<m:t>g</m:t>
</m:r>
</m:e>
</m:acc>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:r>
<m:t>h</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:acc>
<m:accPr>
<m:chr m:val="˚" />
</m:accPr>
<m:e>
<m:r>
<m:t>i</m:t>
</m:r>
</m:e>
</m:acc>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:acc>
<m:accPr>
<m:chr m:val="˙" />
</m:accPr>
<m:e>
<m:r>
<m:t>j</m:t>
</m:r>
</m:e>
</m:acc>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:acc>
<m:accPr>
<m:chr m:val="¨" />
</m:accPr>
<m:e>
<m:r>
<m:t>k</m:t>
</m:r>
</m:e>
</m:acc>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:acc>
<m:accPr>
<m:chr m:val="⃛" />
</m:accPr>
<m:e>
<m:r>
<m:t>l</m:t>
</m:r>
</m:e>
</m:acc>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:acc>
<m:accPr>
<m:chr m:val="⃜" />
</m:accPr>
<m:e>
<m:r>
<m:t>m</m:t>
</m:r>
</m:e>
</m:acc>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:acc>
<m:accPr>
<m:chr m:val="→" />
</m:accPr>
<m:e>
<m:r>
<m:t>n</m:t>
</m:r>
</m:e>
</m:acc>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>f</m:t>
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<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⁡</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>(</m:t>
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<m:r>
<m:t>g</m:t>
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<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⁡</m:t>
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<m:rPr>
<m:sty m:val="p" />
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<m:t>(</m:t>
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<m:t>x</m:t>
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<m:t>)</m:t>
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<m:t>)</m:t>
</m:r>
<m:r>
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<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:sSup>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
</m:e>
<m:sup>
<m:r>
<m:t>3</m:t>
</m:r>
</m:sup>
</m:sSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:sSup>
<m:e>
<m:r>
<m:t>x</m:t>
</m:r>
</m:e>
<m:sup>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sup>
</m:sSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:sSup>
<m:e>
<m:r>
<m:t>x</m:t>
</m:r>
</m:e>
<m:sup>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sup>
</m:sSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁢</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val=")" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
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<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
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<m:t>⁡</m:t>
</m:r>
<m:sSup>
<m:e>
<m:r>
<m:t>x</m:t>
</m:r>
</m:e>
<m:sup>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sup>
</m:sSup>
</m:e>
</m:d>
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<m:mr>
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<m:begChr m:val="(" />
<m:endChr m:val=")" />
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<m:grow />
</m:dPr>
<m:e>
<m:sSup>
<m:e>
<m:r>
<m:t>x</m:t>
</m:r>
</m:e>
<m:sup>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sup>
</m:sSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:r>
<m:t>12</m:t>
</m:r>
</m:e>
</m:d>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:r>
<m:t>1234</m:t>
</m:r>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:m>
<m:mPr>
<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
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<m:mr>
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<m:t>x</m:t>
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<m:t>1</m:t>
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<m:t>not</m:t>
</m:r>
</m:e>
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<m:t>here</m:t>
</m:r>
</m:e>
</m:mr>
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<m:sSup>
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</m:e>
<m:sup>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sup>
</m:sSup>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:nor />
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<m:t>merged</m:t>
</m:r>
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<m:e>
<m:r>
<m:t>y</m:t>
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</m:e>
<m:sub>
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<m:t>1</m:t>
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</m:sub>
</m:sSub>
</m:e>
</m:mr>
<m:mr>
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</m:e>
<m:e>
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<m:nor />
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<m:t>The end.</m:t>
</m:r>
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<m:t>−</m:t>
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<m:t>x</m:t>
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<m:t>2</m:t>
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</m:sup>
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<m:r>
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<m:t>+</m:t>
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<m:t>+</m:t>
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<m:r>
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<m:t>⋅</m:t>
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<m:mr>
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<m:t>First line of equation</m:t>
</m:r>
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<m:t>Other middle line of equation</m:t>
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<m:mr>
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<m:t>Last line of equation</m:t>
</m:r>
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<m:t> </m:t>
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<m:sty m:val="p" />
</m:rPr>
<m:t>Antisymmetric</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t> </m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>Triangular</m:t>
</m:r>
</m:e>
</m:mr>
</m:m>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>a</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>≠</m:t>
</m:r>
<m:r>
<m:t>b</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>≠</m:t>
</m:r>
<m:r>
<m:t>x</m:t>
</m:r>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>c</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>≮</m:t>
</m:r>
<m:r>
<m:t>d</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>≮</m:t>
</m:r>
<m:r>
<m:t>y</m:t>
</m:r>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>e</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>≯</m:t>
</m:r>
<m:r>
<m:t>f</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>≯</m:t>
</m:r>
<m:r>
<m:t>11</m:t>
</m:r>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>g</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∉</m:t>
</m:r>
<m:r>
<m:t>h</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∉</m:t>
</m:r>
<m:r>
<m:t>Z</m:t>
</m:r>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>k</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>≁</m:t>
</m:r>
<m:r>
<m:t>l</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>≁</m:t>
</m:r>
<m:r>
<m:t>3</m:t>
</m:r>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>A</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⊄</m:t>
</m:r>
<m:r>
<m:t>B</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⊂</m:t>
</m:r>
<m:r>
<m:t>C</m:t>
</m:r>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>A</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⊈</m:t>
</m:r>
<m:r>
<m:t>B</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⊈</m:t>
</m:r>
<m:r>
<m:t>C</m:t>
</m:r>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>10</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>≢</m:t>
</m:r>
<m:r>
<m:t>11</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>≡</m:t>
</m:r>
<m:r>
<m:t>12</m:t>
</m:r>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>x</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>≰⃥</m:t>
</m:r>
<m:r>
<m:t>y</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>≰⃥</m:t>
</m:r>
<m:r>
<m:t>z</m:t>
</m:r>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:acc>
<m:accPr>
<m:chr m:val="¯" />
</m:accPr>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>lim</m:t>
</m:r>
</m:e>
</m:acc>
<m:r>
<m:t>x</m:t>
</m:r>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:limLow>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>lim</m:t>
</m:r>
</m:e>
<m:lim>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>̲</m:t>
</m:r>
</m:lim>
</m:limLow>
<m:r>
<m:t>x</m:t>
</m:r>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:limLow>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>lim</m:t>
</m:r>
</m:e>
<m:lim>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>→</m:t>
</m:r>
</m:lim>
</m:limLow>
<m:r>
<m:t>x</m:t>
</m:r>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:limLow>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>lim</m:t>
</m:r>
</m:e>
<m:lim>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>←</m:t>
</m:r>
</m:lim>
</m:limLow>
<m:r>
<m:t>x</m:t>
</m:r>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:m>
<m:mPr>
<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:r>
<m:t>x</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:r>
<m:t>y</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:r>
<m:t>z</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:r>
<m:t>k</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:r>
<m:t>m</m:t>
</m:r>
</m:e>
</m:mr>
</m:m>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:m>
<m:mPr>
<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="left" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>College Algebra </m:t>
</m:r>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>Second Edition</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>James Stewart </m:t>
</m:r>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>McMaster Universitiy</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>Lothar Redlin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t> Pennsylvania State University</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>Saleem Watson</m:t>
</m:r>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t> California State University, Long Beach</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>Copyright 1996, ISBN 0 534-33983-2</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>Brooks/Cole Publishing Company</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>An International Thomson Publishing Company</m:t>
</m:r>
</m:e>
</m:mr>
</m:m>
<m:r>
<m:t> </m:t>
</m:r>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="{" />
<m:endChr m:val="}" />
<m:sepChr m:val="↑" />
<m:grow />
</m:dPr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>2</m:t>
</m:r>
</m:den>
</m:f>
</m:num>
<m:den>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>2</m:t>
</m:r>
</m:den>
</m:f>
</m:den>
</m:f>
</m:e>
<m:e>
<m:nary>
<m:naryPr>
<m:chr m:val="∑" />
<m:limLoc m:val="undOvr" />
<m:subHide m:val="0" />
<m:supHide m:val="0" />
</m:naryPr>
<m:sub>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sup>
<m:e>
<m:r>
<m:t>​</m:t>
</m:r>
</m:e>
</m:nary>
</m:e>
</m:d>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="〈" />
<m:endChr m:val="〉" />
<m:sepChr m:val="|" />
<m:grow />
</m:dPr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>2</m:t>
</m:r>
</m:den>
</m:f>
</m:num>
<m:den>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>2</m:t>
</m:r>
</m:den>
</m:f>
</m:den>
</m:f>
</m:e>
<m:e>
<m:nary>
<m:naryPr>
<m:chr m:val="∑" />
<m:limLoc m:val="undOvr" />
<m:subHide m:val="0" />
<m:supHide m:val="0" />
</m:naryPr>
<m:sub>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sup>
<m:e>
<m:r>
<m:t>​</m:t>
</m:r>
</m:e>
</m:nary>
</m:e>
</m:d>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="⌈" />
<m:endChr m:val="⌉" />
<m:sepChr m:val="|" />
<m:grow />
</m:dPr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>2</m:t>
</m:r>
</m:den>
</m:f>
</m:num>
<m:den>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>2</m:t>
</m:r>
</m:den>
</m:f>
</m:den>
</m:f>
</m:e>
<m:e>
<m:nary>
<m:naryPr>
<m:chr m:val="∑" />
<m:limLoc m:val="undOvr" />
<m:subHide m:val="0" />
<m:supHide m:val="0" />
</m:naryPr>
<m:sub>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sup>
<m:e>
<m:r>
<m:t>​</m:t>
</m:r>
</m:e>
</m:nary>
</m:e>
</m:d>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="" />
<m:endChr m:val="" />
<m:sepChr m:val="⇓" />
<m:grow />
</m:dPr>
<m:e />
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="" />
<m:endChr m:val="" />
<m:sepChr m:val="↕" />
<m:grow />
</m:dPr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>2</m:t>
</m:r>
</m:den>
</m:f>
</m:num>
<m:den>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>2</m:t>
</m:r>
</m:den>
</m:f>
</m:den>
</m:f>
</m:e>
<m:e>
<m:nary>
<m:naryPr>
<m:chr m:val="∑" />
<m:limLoc m:val="undOvr" />
<m:subHide m:val="0" />
<m:supHide m:val="0" />
</m:naryPr>
<m:sub>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sup>
<m:e>
<m:r>
<m:t>​</m:t>
</m:r>
</m:e>
</m:nary>
</m:e>
</m:d>
</m:e>
<m:e />
</m:d>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="[" />
<m:endChr m:val="]" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>2</m:t>
</m:r>
</m:den>
</m:f>
</m:num>
<m:den>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>2</m:t>
</m:r>
</m:den>
</m:f>
</m:den>
</m:f>
</m:e>
</m:d>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
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<m:num>
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<m:t>2</m:t>
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<m:num>
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<m:t>2</m:t>
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<m:t>2</m:t>
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<m:den>
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<m:num>
<m:r>
<m:t>1</m:t>
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<m:t>2</m:t>
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<m:num>
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<m:num>
<m:r>
<m:t>1</m:t>
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<m:t>2</m:t>
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<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
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<m:den>
<m:r>
<m:t>2</m:t>
</m:r>
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<m:e>
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<m:num>
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<m:num>
<m:r>
<m:t>1</m:t>
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<m:t>2</m:t>
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<m:r>
<m:t>2</m:t>
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<m:e />
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<m:mr>
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<m:num>
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<m:t>1</m:t>
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<m:t>2</m:t>
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<m:num>
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<m:t>2</m:t>
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<m:mr>
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<m:e>
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<m:num>
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<m:num>
<m:r>
<m:t>1</m:t>
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<m:t>2</m:t>
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<m:den>
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<m:num>
<m:r>
<m:t>1</m:t>
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<m:den>
<m:r>
<m:t>2</m:t>
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<m:e />
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<m:mr>
<m:e>
<m:d>
<m:dPr>
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<m:e>
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<m:num>
<m:f>
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<m:num>
<m:r>
<m:t>1</m:t>
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<m:t>2</m:t>
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<m:num>
<m:r>
<m:t>1</m:t>
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<m:den>
<m:r>
<m:t>2</m:t>
</m:r>
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<m:e />
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<m:mr>
<m:e>
<m:r>
<m:t>A</m:t>
</m:r>
<m:limLow>
<m:e>
<m:limUpp>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>←</m:t>
</m:r>
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<m:lim>
<m:r>
<m:t>n</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:r>
<m:t>μ</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>−</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
</m:lim>
</m:limUpp>
</m:e>
<m:lim>
<m:r>
<m:t> </m:t>
</m:r>
</m:lim>
</m:limLow>
<m:r>
<m:t>B</m:t>
</m:r>
<m:limLow>
<m:e>
<m:limUpp>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>→</m:t>
</m:r>
</m:e>
<m:lim>
<m:r>
<m:t>n</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>±</m:t>
</m:r>
<m:r>
<m:t>i</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>−</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
</m:lim>
</m:limUpp>
</m:e>
<m:lim>
<m:r>
<m:t>T</m:t>
</m:r>
</m:lim>
</m:limLow>
<m:r>
<m:t>C</m:t>
</m:r>
</m:e>
<m:e />
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<m:mr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:rad>
<m:radPr>
<m:degHide m:val="1" />
</m:radPr>
<m:deg />
<m:e>
<m:r>
<m:t>2</m:t>
</m:r>
</m:e>
</m:rad>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:rad>
<m:radPr>
<m:degHide m:val="1" />
</m:radPr>
<m:deg />
<m:e>
<m:r>
<m:t>3</m:t>
</m:r>
</m:e>
</m:rad>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:rad>
<m:radPr>
<m:degHide m:val="1" />
</m:radPr>
<m:deg />
<m:e>
<m:r>
<m:t>4</m:t>
</m:r>
</m:e>
</m:rad>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:rad>
<m:radPr>
<m:degHide m:val="1" />
</m:radPr>
<m:deg />
<m:e>
<m:r>
<m:t>5</m:t>
</m:r>
</m:e>
</m:rad>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:rad>
<m:radPr>
<m:degHide m:val="1" />
</m:radPr>
<m:deg />
<m:e>
<m:r>
<m:t>6</m:t>
</m:r>
</m:e>
</m:rad>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:r>
<m:t>…</m:t>
</m:r>
</m:den>
</m:f>
</m:den>
</m:f>
</m:den>
</m:f>
</m:den>
</m:f>
</m:den>
</m:f>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:rad>
<m:radPr>
<m:degHide m:val="1" />
</m:radPr>
<m:deg />
<m:e>
<m:r>
<m:t>2</m:t>
</m:r>
</m:e>
</m:rad>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:rad>
<m:radPr>
<m:degHide m:val="1" />
</m:radPr>
<m:deg />
<m:e>
<m:r>
<m:t>3</m:t>
</m:r>
</m:e>
</m:rad>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:rad>
<m:radPr>
<m:degHide m:val="1" />
</m:radPr>
<m:deg />
<m:e>
<m:r>
<m:t>4</m:t>
</m:r>
</m:e>
</m:rad>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:rad>
<m:radPr>
<m:degHide m:val="1" />
</m:radPr>
<m:deg />
<m:e>
<m:r>
<m:t>5</m:t>
</m:r>
</m:e>
</m:rad>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:rad>
<m:radPr>
<m:degHide m:val="1" />
</m:radPr>
<m:deg />
<m:e>
<m:r>
<m:t>6</m:t>
</m:r>
</m:e>
</m:rad>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:r>
<m:t>…</m:t>
</m:r>
</m:den>
</m:f>
</m:den>
</m:f>
</m:den>
</m:f>
</m:den>
</m:f>
</m:den>
</m:f>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val="⌋" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>M</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
</m:d>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val="⌋" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>M</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
</m:d>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val="⌋" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>M</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
</m:d>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val="⌋" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>M</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
</m:d>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val="⌋" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>M</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
</m:d>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val="⌋" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>M</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
</m:d>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val="⌋" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>M</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
</m:d>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val="⌋" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>M</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
</m:d>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val="⌋" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>M</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
</m:d>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>M</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>M</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>M</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>M</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>M</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>M</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>M</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>M</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
<m:e />
</m:mr>
<m:mr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>sin</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⁡</m:t>
</m:r>
<m:r>
<m:t>θ</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>M</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
<m:e />
</m:mr>
</m:m>
</m:oMath>
</m:oMathPara>