利用无效小替换求极限公式

$\displaystyle \lim^{}_{x \to 0}{\frac{sinx}{x}} = 1$

$\displaystyle \lim^{}_{x \to 0}{\frac{tanx}{x}} = 1$

$\displaystyle \lim^{}_{x \to 0}{\frac{arctanx}{x}} = 1$

$\displaystyle \lim^{}_{x \to 0}{\frac{arcsinx}{x}} = 1$

$\displaystyle \lim^{}_{x \to 0}{\frac{\ln(1+x)}{x}} = 1$

$\displaystyle \lim^{}_{x \to 0}{\frac{1-cosx}{\frac{1}{2}x^2}} = 1$

$\displaystyle \lim^{}_{x \to 0}{\frac{(1+x)^a-1}{ax}} = 1$

$\displaystyle \lim^{}_{x \to 0}{\frac{e^x-1}{x}} = 1$