1.极限
\(\lim\limits_{x\to 0} \frac{\sin x}{x}\)
\(\lim\limits_{x\to \infty} \left(1+\frac{1}{x}\right)^x\)
\(\lim\limits_{x\to 1} \frac{\ln(x)}{x-1}\)
2.洛必达
\(\lim\limits_{x\to\infty}\frac{x}{\ln(x)}\)
\(\lim\limits_{x\to 0} \frac{\frac{1}{\cos x}-1}{x\tan x}\)
\(\lim\limits_{x\to\infty}\frac{e^x}{x^2}\)
3.极值、最值、驻点拐点
\(f(x)=x^3-3x+2\)
\(f(x)=\sqrt{x^2-4x+13}\)
\(f(x)=(x-1)^3(x+1)^2\)
4.导数、链式求导法、隐函数求导
\(f(x)=x^2\ln(x)\)，求\(f'(x),f''(x)\)
\(f(x) = \sin(x^4+3x)\)，求\(f'(x)\)
\(x^3+y^3=6xy\)，求\(\dfrac{dy}{dx}\)
5.不定积分
\(\int \frac{1}{\sqrt{a^2-x^2}} dx\)
\(\int \frac{x^3+1}{x^2} dx\)
\(\int \frac{\ln(x)}{x} dx\)
6.分布式、定积分
\(f(x)=\begin{cases} x & x<0\ x+1 & x\geq 0 \end{cases}\)，求\(\displaystyle\int_{-1}^1 f(x)dx\)
\(f(x)=\frac{1}{x+1}\)，求\(\displaystyle\int_0^\infty xe^{-ax}f(x)dx\)
\(f(x)=x^2+1\)，求\(\displaystyle\int_0^1 f(x)dx\)