拉格朗日余项 $$ f(x) = f(x\_0) + f'(x\_0)(x-x\_0) + \cdots + \frac{1}{n!}f^{(n)}(x\_0)(x-x\_0)^n + \frac{f^{(n+1)}(\xi)}{(n...

$f(x)f'(x)$的原函数辅助函数$F(x)=f^2(x)$ $\[f'(x)]^2+f(x)f''(x)$的原函数辅助函数$F(x)=f(x)f'(x)$ $f'(x)+f(x)\phi'(x)$的原函数辅助函数$F(x)=f(x...

泰勒展开式 $$ e^x = \sum^\infty\_{n=0}\frac{x^n}{n!} = 1 + x + \frac{x^2}{2!} + \cdots $$ $$ \frac{1}{x+1} = \sum^\infty\_{...

$$ \sin x = x - \frac{x^3}{3!} + o(x^3) $$ $$ \cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} + o(x^4) $$ $$ \arcsin x = ...

$$ \lim\_{x \to 0}\sin x \sim x \\ \lim\_{x \to 0}\tan x \sim x \\ \lim\_{x \to 0}\arcsin x \sim x \\ \lim\_{x \to 0}\ar...