f ( x ) = x 2 {\displaystyle f(x)=x^{2}}
f ( x ) {\displaystyle f(x)\,\!} = ∑ n = 0 ∞ a n x n {\displaystyle =\sum _{n=0}^{\infty }a_{n}x^{n}} = a 0 + a 1 x + a 2 x 2 + ⋯ {\displaystyle =a_{0}+a_{1}x+a_{2}x^{2}+\cdots }
( 1 2 ) n {\displaystyle \left({\frac {1}{2}}\right)^{n}}
x = − b ± b 2 − 4 a c 2 a {\displaystyle x={\frac {{\color {Blue}-b}\pm {\sqrt {\color {Red}b^{2}-4ac}}}{\color {Green}2a}}}
∑ m = 1 ∞ ∑ n = 1 ∞ m 2 n 3 m ( m 3 n + n 3 m ) {\displaystyle \sum _{m=1}^{\infty }\sum _{n=1}^{\infty }{\frac {m^{2}n}{3^{m}\left(m3^{n}+n3^{m}\right)}}}
| z ¯ | = | z | , | ( z ¯ ) n | = | z | n , arg ( z n ) = n arg ( z ) {\displaystyle |{\bar {z}}|=|z|,|({\bar {z}})^{n}|=|z|^{n},\arg(z^{n})=n\arg(z)}
2 Fe 3 O 4 ⏞ magnetite + 1 2 O 2 ⟶ 3 ( λ − Fe 2 O 3 ) ⏞ maghemite 2 Fe 3 O 4 ⏟ magnetite + 1 2 O 2 ⟶ 3 ( α − Fe 2 O 3 ) ⏟ hematite {\displaystyle {\begin{aligned}\overbrace {{\ce {2Fe3O4}}} ^{\text{magnetite}}+{\ce {1/2 O2 ->}}\ &{\color {Brown}\overbrace {{\ce {3(\lambda{-}Fe2O3)}}} ^{\text{maghemite}}}\\\underbrace {{\ce {2Fe3O4}}} _{\text{magnetite}}+{\ce {1/2 O2 ->}}\ &{\color {Red}\underbrace {{\ce {3(\alpha{-}Fe2O3)}}} _{\text{hematite}}}\end{aligned}}}
(1)
f ( x ) = { 1 − 1 ≤ x < 0 1 2 x = 0 1 − x 2 otherwise {\displaystyle f(x)={\begin{cases}1&-1\leq x<0\\{\frac {1}{2}}&x=0\\1-x^{2}&{\text{otherwise}}\end{cases}}}
( a b c d ) {\displaystyle \left({\begin{array}{cc}a&b\\c&d\end{array}}\right)}
∫ ln ( x ) 3 d x = x ln ( x ) 3 − 3 ∫ ln ( x ) 2 d x {\displaystyle {\begin{aligned}\int \ln(x)^{3}dx=x\ln(x)^{3}-3\int \ln(x)^{2}dx\end{aligned}}}
