\begin{matrix} 2 \sum a b \\ x^{' 3} \\ f^{'} (x) + sin cos θ = 1 \\ f (z) = \sum_{n = 0}^{\infty} a_{n} z^{n}, | z | < R ​ (R \neq 0) \\ \int_{C} (\sum_{n = 0}^{\infty} a_{n} z^{n}) ⅆ z = \sum_{n = 0}^{\infty} a_{n} \int_{C} z^{n} ⅆ z \\ lim_{n \to \infty} | \int_{C} [f (z) - \sum_{k = 0}^{n} a_{k} z^{k}] ⅆ z | = 0 \\ n \geq N (ε) \Rightarrow | f (z) - \sum_{k = 0}^{n} a_{k} z^{k} | < ε \\ 10 Bq + 10 Ci \\ 10 amol + 10 Emol - 10 fmol + 10 Gmol - 10 kmol + 10 Mmol \\ 10 μmol + 10 mmol - 10 mol + 10 nmol - 10 Pmol + 10 pmol - 10 Tmol \\ 10 acre + 10 hectare - 10 {ft}^{2} + 10 {in}^{2} - 10 m^{2} \\ 10 A + 10 kA - 10 μA + 10 mA - 10 nA \\ 10 F + 10 μF - 10 mF + 10 nF - 10 pF \\ 10 C + 1.0 m/s/s - 0.1 m / s^{2} \\ 10 kS + 10 μS - 10 mS + 10 S \\ 10 kV + 10 MV - 10 μV + 10 mV - 10 nV + 10 pV - 10 V \\ 10 GΩ + 10 kΩ - 10 MΩ + 10 mΩ - 10 Ω \\ 10 Btu + 10 cal - 10 eV + 10 erg - 10 GeV + 10 GJ \\ 10 J + 10 kcal - 10 kJ + 10 MeV - 10 MJ + 10 μJ - 10 mJ + 10 nJ \\ 10 dyn + 10 kN - 10 MN + 10 μN - 10 mN + 10 N - 10 ozf + 10 lbf \\ 10 EHz + 10 GHz - 10 Hz + 10 kHz - 10 MHz + 10 PHz - 10 THz \\ 10 fc + 10 lx - 10 phot \\ 10 Å + 10 am - 10 cm + 10 dm - 10 fm + 10 ft - 10 in \\ 10 km + 10 m - 10 μm + 10 mi - 10 mm + 10 nm - 10 pm \\ 10 sb \\ 10 lm \\ 10 cd \\ 10 Mx + 10 μWb - 10 mWb + 10 nWb - 10 Wb \\ 10 G + 10 μT - 10 mT + 10 nT - 10 pT + 10 T \\ 10 H + 10 μH - 10 mH \\ 10 u + 10 cg - 10 dg + 10 g - 10 kg + 10 μg - 10 mg + 10 lb - 10 slug \\ 10 ° + 10 μrad - 10 mrad + 10^{′} - 10 rad + 10^{′′} \\ 10 GW + 10 hp - 10 kW + 10 MW - 10 μW + 10 mW - 10 nW + 10 W \\ 10 atm + 10 bar - 10 kbar + 10 kPa - 10 MPa + 10 μPa - 10 mbar + 10 mmHg - 10 Pa + 10 torr \\ 10 sr \\ 10 °C + 10 °F - 10 K \\ 10 as + 10 d - 10 fs + 10 h - 10 μs + 10 ms - 10 min + 10 ns - 10 ps + 10 s - 10 y \\ 10 {ft}^{3} + 10 {in}^{3} - 10 m^{3} + 10 gal - 10 l \\ 10 ml + 10 pint - 10 qt \\ \frac{1}{x (y)} = (- \int e^{- \frac{1}{2} y^{2}} sin y ⅆ y + C_{1}) e^{\frac{1}{2} y^{2}} \\ ⅅ_{x} y - y = sin x \\ (\frac{1}{2}) (\frac{1}{2}) (\frac{1}{2}) \\ [\frac{1}{2}] (\frac{1}{2}) {\frac{1}{2}} \\ 〈 \frac{1}{2} 〉 ⌊ \frac{1}{2} ⌋ ⌈ \frac{1}{2} ⌉ \\ ↑ \frac{1}{2} ↑ ↓ \frac{1}{2} ↓ ↕ \frac{1}{2} ↕ \\ \frac{1}{2} \frac{1}{2} \frac{1}{2} \\ \frac{1}{2} \frac{1}{2} \frac{1}{2} \\ \frac{1}{2} \frac{1}{2} \frac{1}{2} \\ - (a - b) = b - a \\ \frac{2}{5} + \frac{3}{7} = \frac{2 \cdot 7 + 3 \cdot 5}{35} = \frac{29}{35} \\ | a | = {\begin{matrix} a & if & a \geq 0 \\ - a & if & a < 0 \end{matrix} \\ a^{n} = \underset{n factors}{\underset{︸}{a \cdot a \cdot \dots \cdot a}} \\ {(\frac{a}{b})}^{- n} = {(\frac{b}{a})}^{n} \\ \sqrt[n]{a} = b means b^{n} = a . \\ \sqrt[4]{\frac{16}{81}} = \frac{\sqrt[4]{16}}{\sqrt[4]{81}} = \frac{2}{3} \\ {x ∣ x \neq 0, x \neq 1} \\ a_{n} x^{n} + a_{n - 1} x^{n - 1} + \dots + a_{1} x + a_{0} \\ a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2}) \\ {(x + y)}^{2} \\ H = {(\begin{matrix} a & b \\ c & d \end{matrix}) \in G ∣ a d - b c = 1} \\ | x | + || y || + {z} - [a c] + (b) = [a, b] \\ x = 1 \\ x = 1 \\ x = 1 \\ x = 1 \\ [- \frac{10}{3}, - \frac{7}{3}) \cup (- \frac{7}{3}, - \frac{4}{3}] \\ A \frac{\partial u}{\partial x} + B \frac{\partial u}{\partial y} + C u = E \\ \sum_{}^{} x \\ \sum_{\begin{matrix} 1 < i < 10 \\ 1 < j < 10 \end{matrix}}^{} 2^{i + j} \\ Γ_{1_{^{\begin{matrix} 2_{^{\begin{matrix} 3 \\ 4 \end{matrix}}}^{} \\ 5_{^{\begin{matrix} 6 \\ 7 \end{matrix}}}^{} \end{matrix}}}^{}}^{1^{\begin{matrix} 5^{\begin{matrix} 7 \\ 6 \end{matrix}} \\ 2^{\begin{matrix} 4 \\ 3 \end{matrix}} \end{matrix}}} \\ y (x) = \frac{x e^{x} - e^{x} + 2}{e^{x}} = x - 1 + \frac{2}{e^{x}} \\ \begin{matrix} ⅅ_{x ​ x} y - y = 0 \\ y (0) = 1 \\ y^{'} (0) = 0 \end{matrix} \\ y (x) = \frac{1}{3} e^{- \sqrt[3]{(- 1)} x} + \frac{2}{3} e^{\frac{1}{2} \sqrt[3]{(- 1)} x} cos \frac{1}{2} \sqrt{3} \sqrt[3]{(- 1)} x \\ y (t) = 2 tan (2 t - \frac{1}{4} π) \\ ℱ (\begin{matrix} e^{2 π i x} \\ 2 π Dirac (x - 2 π) \end{matrix}, x, s) = (\begin{matrix} 2 π Dirac (s - 2 π) \\ 2 π e^{- 2 i π s} \end{matrix}) \\ \begin{matrix} x = 1 \\ x + 3 = 123 \end{matrix} \\ \begin{matrix} t & x & y & z \\ 0 & 1.0000 & 1.0000 & 1.0000 \\ .1 & 1.1158 & 1.0938 & .8842 \\ .2 & 1.2668 & 1.1695 & .7332 \\ .3 & 1.4582 & 1.2173 & .5418 \\ .4 & 1.6953 & 1.2253 & .3047 \\ .5 & 1.9830 & 1.1791 & .0170 \\ .6 & 2.3256 & 1.0619 & - .3256 \\ .7 & 2.7265 & .8542 & - .7265 \\ .8 & 3.1873 & .5344 & - 1.1873 \\ .9 & 3.7077 & .0777 & - 1.7077 \\ 1.0 & 4.2842 & - .5424 & - 2.2842 \end{matrix} \\ K_{v} (z) = {BesselK}_{v} (z) \\ z^{2} \frac{ⅆ^{2} w}{ⅆ z^{2}} + z \frac{ⅆ w}{ⅆ z} - (z^{2} + v^{2}) w = 0 \\ \frac{\partial^{2} u (x, y)}{\partial x^{2}} - \frac{\partial^{2} u (x, y)}{\partial y^{2}} = 0 \\ y (t, x) = F_{1} (- x - a t) + F_{2} (x - a t) \\ \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{matrix} \\ 2 x + 1 = 5 \\ \begin{matrix} 1 = 3 \\ 9 = 7 \end{matrix} \\ \begin{matrix} a b \\ c d \\ e f \end{matrix} \\ \begin{matrix} x + 2 y - 3 = 5 \\ 4 x - y - 5 = 98 \end{matrix} \\ \begin{matrix} x = z \\ 1 = 3 \end{matrix} \\ \begin{matrix} A_{1} = N_{0} (λ; Ω^{'}) - φ (λ; Ω^{'}), \\ A_{2} = φ (λ; Ω^{'}) - φ (λ; Ω), \\ A_{3} = 𝒩 (λ; ω) . \end{matrix} \\ \begin{matrix} sin θ \\ cos γ \end{matrix} \\ x = {\begin{matrix} x & if x < 0 \\ - x & if x \geq 0 \end{matrix} \\ \begin{matrix} L M R M \\ L M R M \end{matrix} \\ \begin{matrix} M A T H \\ M A T H \end{matrix} \\ ⋮ \\ \nabla\times F = 0 \\ \nabla\cdot F \\ \nabla\cdot\nabla F = \nabla^{2} F + 7 = A \\ \nabla\times (x y, y z, z x) = [\begin{matrix} - y \\ - z \\ - x \end{matrix}] \\ \nabla\times (y, z, x) = (- 1, - 1, - 1) \neq 0 \\ x + y + α = 102 \\ 𝐚 + 𝐛 = 𝐜 \\ x + 1 \\ x + f (𝐱) - 1 = 123 \\ 𝑇 h 𝑒 𝑞 𝑢 𝑖 𝑐 𝑘 b r o w n f o x j u m p s 𝐨 𝐯 𝐞 𝐫 t h e 𝗅 𝖺 𝗓 𝗒 𝚍 𝚘 𝚐 . T h e e n d . \\ (\frac{\partial f}{\partial x_{1}} (c_{1}, c_{2}, \dots, c_{n}), \frac{\partial f}{\partial x_{2}} (c_{1}, c_{2}, \dots, c_{n}), \dots, \frac{\partial f}{\partial x_{n ​ 1}} (c_{1}, c_{2}, \dots, c_{n})) \\ \nabla (c u v + v^{2} w) = (u v, c v, c u + 2 v w, v^{2}) \\ \begin{matrix} D_{u} f (a, b, c) = \nabla f (a, b, c) \cdot 𝐮 \\ = \frac{\partial f}{\partial x} (a, b, c) u_{1} + \frac{\partial f}{\partial y} (a, b, c) u_{2} + \frac{\partial f}{\partial z} (a, b, c) u_{3} \end{matrix} \\ θ \in {π + 2 X_{3} π - (arccos \frac{1}{7} \sqrt{14}) | X_{3} \in ℤ}, θ \in {2 X_{4} π - π + (arccos \frac{1}{7} \sqrt{14}) | X_{4} \in ℤ} \\ P = A {(A^{T} A)}^{- 1} A^{T} \\ det (\begin{matrix} x & y & 1 \\ a & b & 1 \\ a & d & 1 \end{matrix}) = x b - x d + a d - a b = 0 \\ A (θ) A (- θ) = [\begin{matrix} cos θ & - sin θ \\ sin θ & cos θ \end{matrix}] [\begin{matrix} cos θ & sin θ \\ - sin θ & cos θ \end{matrix}] \\ J (A) = [\begin{matrix} J_{n_{1}} (λ_{1}) & 0 & \dots & 0 \\ 0 & J_{n_{2}} (λ_{2}) & \dots & 0 \\ ⋮ & ⋮ & ⋱ & ⋮ \\ 0 & 0 & \dots & J_{n_{k}} (λ_{k}) \end{matrix}] \\ det (\begin{matrix} - 4 + X & - 1 & 0 \\ 0 & - 4 + X & 0 \\ 0 & 0 & - 4 + X \end{matrix}) = {(X - 4)}^{3} \\ {(\begin{matrix} - \frac{1}{2} - \frac{1}{6} \sqrt{33} \\ 1 \end{matrix})} \leftrightarrow \frac{5}{2} - \frac{1}{2} \sqrt{33} \\ ∥ A ∥ = max_{x \neq 0} \frac{∥ A x ∥}{∥ x ∥} \\ (\begin{matrix} a_{1 ​ 1} & a_{1 ​ 2} \\ a_{2 ​ 1} & a_{2 ​ 2} \end{matrix}) + (\begin{matrix} b_{1 ​ 1} & b_{1 ​ 2} \\ b_{2 ​ 1} & b_{2 ​ 2} \end{matrix}) = (\begin{matrix} a_{1 ​ 1} + b_{1 ​ 1} & a_{1 ​ 2} + b_{1 ​ 2} \\ a_{2 ​ 1} + b_{2 ​ 1} & a_{2 ​ 2} + b_{2 ​ 2} \end{matrix}) \\ f ([\begin{matrix} 1 & 2 \\ 4 & 3 \end{matrix}]) = {[\begin{matrix} 1 & 2 \\ 4 & 3 \end{matrix}]}^{2} - 5 [\begin{matrix} 1 & 2 \\ 4 & 3 \end{matrix}] - 2 = [\begin{matrix} 2 & - 2 \\ - 4 & 0 \end{matrix}] \\ x = lim_{x = 1} \sum_{1}^{2} a \\ \int_{a}^{b} f (x) ⅆ x = lim_{∥ P ∥ \to 0} \sum_{i = 1}^{n} f ({\bar{x}}_{i}) Δ x_{i} \\ \int_{a}^{b} f (x) ⅆ x = lim_{n \to \infty} \frac{b - a}{n} \sum_{i = 1}^{n} f (a + i \frac{b - a}{n}) \\ \int_{0}^{2} x^{5} \sqrt{x^{3} + 1} ⅆ x = \int_{1}^{3} \frac{2}{3} u \frac{\sqrt{(u^{2})}}{{(u^{2} - 1)}^{\frac{2}{3}}} (u^{2} {(u^{2} - 1)}^{\frac{2}{3}} - {(u^{2} - 1)}^{\frac{2}{3}}) ⅆ u \\ \int f (g (x)) g^{'} (x) ⅆ x = \int f (u) ⅆ u \\ x = 2 \sum_{n = 1}^{100} n (n - 1) \\ lim_{x \to 0} sin (\frac{1}{x}) = - 1 .. 1 \\ h (i, j) = (2 - j) g (i) + (j - 1) f (g (i)) \\ △ : [0, 1] \to [0, 1] \\ 0 ▽ x = x \\ x △ y = h^{- 1} (h (x) h (y)) \\ x △ y = f^{- 1} (max {f (x) + f (y) - 1, 0}) \\ x ▽ y = η (η (x) △ η (y)) \\ x △_{0} y = {\begin{matrix} x \land y & if & x \lor y = 1 \\ 0 & if & x \lor y < 1 \end{matrix} \\ lim_{a \to 1^{+}} {log}_{a} [1 + \frac{(a^{x} - 1) (a^{y} - 1)}{a - 1}] = lim_{a \to 1^{-}} {log}_{a} [1 + \frac{(a^{x} - 1) (a^{y} - 1)}{a - 1}] = x y \\ g (x) = exp (- \frac{1 - {(1 - x)}^{a}}{(2^{a} - 1) {(1 - x)}^{a}}) \\ Aut (𝐈) = {f : [0, 1] \to [0, 1] | \begin{matrix} f is one-to-one and onto, and \\ x \leq y implies f (x) \leq f (y) \end{matrix}} \\ x^{2} + y^{2} = r^{2}, tan θ = \frac{y}{x} \\ \sqrt{2} \sqrt{1 - t^{2}} \\ [(2 + sin t) 10 cos t, (2 + cos t) 10 sin t, 3 sin 3 t] \\ {t = 0, s = 0}, {t = π, s = π} \\ \begin{matrix} \begin{matrix} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ 2 & 4 & 6 & 8 & 10 & 1 & 3 & 5 & 7 & 9 \\ 3 & 6 & 9 & 1 & 4 & 7 & 10 & 2 & 5 & 8 \\ 4 & 8 & 1 & 5 & 9 & 2 & 6 & 10 & 3 & 7 \\ 5 & 10 & 4 & 9 & 3 & 8 & 2 & 7 & 1 & 6 \\ 6 & 1 & 7 & 2 & 8 & 3 & 9 & 4 & 10 & 5 \\ 7 & 3 & 10 & 6 & 2 & 9 & 5 & 1 & 8 & 4 \\ 8 & 5 & 2 & 10 & 7 & 4 & 1 & 9 & 6 & 3 \\ 9 & 7 & 5 & 3 & 1 & 10 & 8 & 6 & 4 & 2 \\ 10 & 9 & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 \end{matrix} \end{matrix} \\ \begin{matrix} testing x^{2} end. \end{matrix} \\ \begin{matrix} x \end{matrix} \\ \begin{matrix} x \end{matrix} \\ \begin{matrix} x \end{matrix} \\ \begin{matrix} x \end{matrix} \\ \frac{ⅆ f}{ⅆ x} (x_{1}) = 5 \\ \int x ⅆ x = \iint x y ⅆ x ⅆ y = ∭ x y z ⅆ x ⅆ y ⅆ z = ⨌ x y z t ⅆ x ⅆ y ⅆ z ⅆ t \\ mod a \\ 5 mod 3 = 2 \\ f (0) mod 3 = 1 \\ 5 x + 4 \equiv 8 ​ (mod 13) \\ a = (5 - 3) / 5 mod 7 = 6 \\ (2 x^{2} + x + 2) + (2 x + 1) mod 3 = 2 x^{2} \\ \begin{matrix} + & 0 & 1 \\ 000 & 000 & 111 \\ 1 & 1 & 0 \end{matrix} \\ 4. 974 9 \\ \frac{ⅆ}{ⅆ x} F (x) \\ [86.333, 146.33, 129.33] \\ BinomialDist (x; n, p) = \sum_{k = 0}^{x} (\frac{n}{k}) p^{k} q^{n - k} \\ Pr (X \leq 54) = BinomialDist (54; 100, .55) = .45846 \\ k = max {| \frac{\partial f}{\partial y} (x, y) | : (x, y) \in D} . \\ m = lim_{x \overset{}{\to} a} \frac{f (x) - f (a)}{x - a} \\ | A | = | \begin{matrix} a_{1 ​ 1} & a_{1 ​ 2} & \cdot & \cdot & \cdot & a_{1 ​ n} \\ a_{2 ​ 1} & a_{2 ​ 2} & \cdot & \cdot & \cdot & a_{2 ​ n} \\ \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot & \cdot \\ a_{n ​ 1} & a_{n ​ 2} & \cdot & \cdot & \cdot & a_{n ​ n} \end{matrix} | = a_{1 ​ 1} A_{1 ​ 1} + a_{1 ​ 2} A_{1 ​ 2} + \dots + a_{1 ​ n} A_{1 ​ n} \\ x = 1 (hl text x end.) \\ x = 1 (hl to URI x end) \\ x = 1 (sex) \\ x = 1 (jbm) \\ f (x) g [y] h {z} + ⌊ a ⌋ ⌈ b ⌉ 〈 c 〉 \\ \frac{123}{\frac{456}{A}} | ∥ \frac{A}{\frac{B}{A}} / \frac{1}{\frac{2}{A}} / (\frac{3}{\frac{4}{A}}) ↕ \frac{5}{\frac{6}{A}} ↕ \frac{7}{\frac{8}{A}} ⇕ \frac{\frac{9}{20}}{\frac{10}{A}} ⇕ ↑ \frac{11}{\frac{12}{A}} ↑ ⇑ \frac{13}{\frac{14}{A}} ⇑ ↓ \frac{15}{\frac{16}{A}} ↓ ⇓ \frac{17}{\frac{18}{A}} ⇓ \\ x \begin{matrix} x & x \\ x & x \end{matrix} x \\ (a_{1}, a_{2}, \dots, a_{n}) \cdot (b_{1}, b_{2}, \dots, b_{n}) = a_{1} b_{1}^{*} + a_{2} b_{2}^{*} + \dots + a_{n} b_{n}^{*} \\ ⌊ \frac{n}{5} ⌋ + ⌊ \frac{n}{5^{2}} ⌋ + ⌊ \frac{n}{5^{3}} ⌋ + ⌊ \frac{n}{5^{4}} ⌋ + \dots \\ x_{1} + \dots + x_{n} \\ \underset{k times}{\underset{︸}{x + \dots + x}} \\ \sqrt[n]{x_{1} x_{2} \dots x_{n}} \\ n! = 1 \times 2 \times 3 \times 4 \times \dots \times n \\ P : a = x_{0} < x_{1} < x_{2} < \dots < x_{n} = b \\ f (x) = \frac{30}{13 cos x} + \frac{10}{3} \sqrt{(100 + \frac{9}{{cos}^{2} x} - \frac{60}{cos x} sin (x + \frac{29}{90} π))} \\ \int cos (A x) sin (B x) ⅆ x = \frac{- cos (B - A) x}{2 (B - A)} + \frac{- cos (B + A) x}{2 (B + A)} + C . \\ 235.3 + 813 = 1048. 3 \\ max_{- 2 \leq x \leq 2} (x^{3} - 6 x + 3) = 8.0 \\ x decade = 2 century \\ \frac{ⅆ^{5} (x^{7} - 3 x^{6})}{ⅆ x^{5}} \frac{ⅆ^{n} sin x}{ⅆ x^{n}} \frac{ⅆ^{3}}{ⅆ x^{3}} f (x) \frac{ⅆ^{2}}{ⅆ t^{2}} (4 t^{5} - 3 t) \\ f (x) = \frac{30}{13 cos x} + \frac{10}{3} \sqrt{(100 + \frac{9}{{cos}^{2} x} - \frac{60}{cos x} sin (x + \frac{29}{90} π))} \\ \int_{𝐑^{3}} (\frac{{| u_{1} |}^{2} + {| \nabla u_{0} |}^{2}}{2} + \frac{{| u_{0} |}^{6}}{6}) ⅆ x < \infty \\ (\nabla\times 𝐅) \cdot 𝐤 = z + 1 \\ M \frac{M^{\frac{M}{M}}}{M} \\ ⅅ_{x} x^{2} ⅅ_{x} (x^{2}) ⅅ_{x ​ x} (x^{2}) ⅅ_{x^{2}} (x^{2}) ⅅ_{x ​ y} (x^{2} y^{3}) ⅅ_{x^{s} ​ y^{t}} (x^{2} y^{3}) \\ 5 24! x^{6} \\ \begin{matrix} \begin{matrix} x + \sqrt[2]{\frac{a^{y - 1}}{12.34}} & sin θ \\ 1 \end{matrix} \end{matrix} \\ \begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix} \\ (\begin{matrix} 0 & - i \\ i & 0 \end{matrix}) \\ [\begin{matrix} 1 & 0 \\ 0 & - 1 \end{matrix}] \\ | \begin{matrix} a & b \\ c & d \end{matrix} | \\ ∥ \begin{matrix} 1 & 0 & 1 \\ 0 & 11 \end{matrix} ∥ \\ \begin{matrix} 1 & 2 & 3 \\ 4 & 5 \end{matrix} \\ testing \begin{matrix} sin θ \end{matrix} \\ \hat{a} + \overset{ˇ}{b} + \tilde{c} + \overset{´}{d} + \overset{`}{e} + \overset{˘}{f} + \bar{g} + h + \overset{˚}{i} + \dot{j} + \ddot{k} + \overset{⃛}{l} + \overset{⃜}{m} + \vec{n} \\ f (g (x)) = {sin}^{3} x^{2} + sin x^{2} sin (sin x^{2}) \\ (x^{2} + 12) + 1234 \\ \begin{matrix} x = 1 & not & here \\ x^{2} & merged & y_{1} \\ jbm & lowlife & The end. \end{matrix} \\ x^{2} + y^{2} = z^{2} - 1 \\ \begin{matrix} x^{2} + y^{2} = z^{2} - 1 \\ x + y^{3} = z^{3} \end{matrix} \\ \begin{matrix} x^{2} + y^{2} = z^{2} - 1 \\ x + y^{3} = z^{3} \end{matrix} \\ \begin{matrix} x^{2} + y^{2} = 1 \\ x = \sqrt{1 - y^{2}} \end{matrix} \\ \begin{matrix} {(a + b)}^{2} = a^{2} + 2 a b + b^{2} \\ (a + b) \cdot (a - b) = a^{2} - b^{2} \end{matrix} \\ \begin{matrix} First line of equation \\ Middle line of equation \\ Other middle line of equation \\ Last line of equation \end{matrix} \\ \begin{matrix} L_{1} = R_{1} L_{2} = R_{2} \\ L_{3} = R_{3} L_{4} = R_{4} \end{matrix} \\ \begin{matrix} {(a + b)}^{4} = {(a + b)}^{2} {(a + b)}^{2} \\ = (a^{2} + 2 a b + b^{2}) (a^{2} + 2 a b + b^{2}) \\ = a^{4} + 4 a^{3} b + 6 a^{2} b^{2} + 4 a b^{3} + b^{4} \end{matrix} \\ \begin{matrix} x^{2} + y^{2} = 1 \\ x = \sqrt{1 - y^{2}} \end{matrix} \begin{matrix} {(a + b)}^{2} = a^{2} + 2 a b + b^{2} \\ (a + b) \cdot (a - b) = a^{2} - b^{2} \end{matrix} \\ \begin{matrix} Vertex & V (0, 0) \\ Focus & F (0, p) \\ Directrix & y = - p \end{matrix} \\ \frac{ⅆ}{ⅆ x} ({csc}^{- 1} x) = - \frac{1}{| x | \sqrt{x^{2} - 1}} \\ {tanh}^{- 1} x = \frac{1}{2} ln (\frac{1 + x}{1 - x}) - 1 < x < 1 \\ ∠ α + ∠ A B C + ∠ 1 = ▵ a b c \\ y = e^{- \int P ⅆ x} [\int e^{\int P ⅆ x} Q ⅆ x + c] \\ x = 1 + y^{3} & x = 1 + y \\ $ 1.00 + 25 ¢ - 3 £ + 2.45 ¤ - 0.7 ¥ - a ₠ + 20 ₣ + 30 ₤ - 4.56 ₧ \\ \begin{matrix} 2 x + y = 3 \\ 3 x - 4 y = 5 \\ a + b = c + 12345 \end{matrix} \\ \begin{matrix} Unrestricted & Symmetric & Antisymmetric & Triangular \end{matrix} \\ a \neq b \neq x \\ c ≮ d ≮ y \\ e ≯ f ≯ 11 \\ g \notin h \notin Z \\ k ≁ l ≁ 3 \\ A ⊄ B \subset C \\ A ⊈ B ⊈ C \\ 10 ≢ 11 \equiv 12 \\ x ≰⃥ y ≰⃥ z \\ lim^{¯} x \\ lim_{̲} x \\ lim_{\to} x \\ lim_{\leftarrow} x \\ \begin{matrix} x = y + z \\ = k + m \end{matrix} \\ \begin{matrix} College Algebra Second Edition \\ James Stewart McMaster Universitiy \\ Lothar Redlin Pennsylvania State University \\ Saleem Watson California State University, Long Beach \\ Copyright 1996, ISBN 0 534-33983-2 \\ Brooks/Cole Publishing Company \\ An International Thomson Publishing Company \end{matrix} \\ {\frac{\frac{1}{2}}{\frac{1}{2}} ↑ \sum_{1}^{2}} \\ 〈 \frac{\frac{1}{2}}{\frac{1}{2}} | \sum_{1}^{2} 〉 \\ ⌈ \frac{\frac{1}{2}}{\frac{1}{2}} | \sum_{1}^{2} ⌉ \\ ⇓ \frac{\frac{1}{2}}{\frac{1}{2}} ↕ \sum_{1}^{2} ⇓ \\ [\frac{\frac{1}{2}}{\frac{1}{2}}] \\ (\frac{\frac{1}{2}}{\frac{1}{2}}) \\ {\frac{\frac{1}{2}}{\frac{1}{2}}} \\ 〈 \frac{\frac{1}{2}}{\frac{1}{2}} 〉 \\ ⌊ \frac{\frac{1}{2}}{\frac{1}{2}} ⌋ \\ ⌈ \frac{\frac{1}{2}}{\frac{1}{2}} ⌉ \\ ↑ \frac{\frac{1}{2}}{\frac{1}{2}} ↑ \\ ↓ \frac{\frac{1}{2}}{\frac{1}{2}} ↓ \\ ↕ \frac{\frac{1}{2}}{\frac{1}{2}} ↕ \\ ⇑ \frac{\frac{1}{2}}{\frac{1}{2}} ⇑ \\ ⇓ \frac{\frac{1}{2}}{\frac{1}{2}} ⇓ \\ ⇕ \frac{\frac{1}{2}}{\frac{1}{2}} ⇕ \\ \frac{\frac{1}{2}}{\frac{1}{2}} \\ \arrowvert \frac{\frac{1}{2}}{\frac{1}{2}} \arrowvert \\ \Arrowvert \frac{\frac{1}{2}}{\frac{1}{2}} \Arrowvert \\ \bracevert \frac{\frac{1}{2}}{\frac{1}{2}} \bracevert \\ | \frac{\frac{1}{2}}{\frac{1}{2}} | \\ | \frac{\frac{1}{2}}{\frac{1}{2}} | \\ | \frac{\frac{1}{2}}{\frac{1}{2}} | \\ ∥ \frac{\frac{1}{2}}{\frac{1}{2}} ∥ \\ ∥ \frac{\frac{1}{2}}{\frac{1}{2}} ∥ \\ / \frac{\frac{1}{2}}{\frac{1}{2}} / \\ \ \frac{\frac{1}{2}}{\frac{1}{2}} \ \\ ⎱ \frac{\frac{1}{2}}{\frac{1}{2}} ⎰ \\ \lgroup \frac{\frac{1}{2}}{\frac{1}{2}} \rgroup \\ ⌞ \frac{\frac{1}{2}}{\frac{1}{2}} ⌟ \\ ⌜ \frac{\frac{1}{2}}{\frac{1}{2}} ⌝ \\ A \leftarrow_{}^{n + μ - 1} B \to_{T}^{n \pm i - 1} C \\ \frac{1}{\sqrt{2} + \frac{1}{\sqrt{3} + \frac{1}{\sqrt{4} + \frac{1}{\sqrt{5} + \frac{1}{\sqrt{6} + \dots}}}}} \\ \frac{1}{\sqrt{2} + \frac{1}{\sqrt{3} + \frac{1}{\sqrt{4} + \frac{1}{\sqrt{5} + \frac{1}{\sqrt{6} + \dots}}}}} \\ (\frac{sin θ}{M} ⌋ \\ (\frac{sin θ}{M} ⌋ \\ (\frac{sin θ}{M} ⌋ \\ (\frac{sin θ}{M} ⌋ \\ (\frac{sin θ}{M} ⌋ \\ (\frac{sin θ}{M} ⌋ \\ (\frac{sin θ}{M} ⌋ \\ (\frac{sin θ}{M} ⌋ \\ (\frac{sin θ}{M} ⌋ \\ \frac{sin θ}{M} \\ \frac{sin θ}{M} \\ \frac{sin θ}{M} \\ \frac{sin θ}{M} \\ \frac{sin θ}{M} \\ \frac{sin θ}{M} \\ \frac{sin θ}{M} \\ \frac{sin θ}{M} \\ \frac{sin θ}{M} \end{matrix}