قاعده هوپیتال

${\displaystyle \lim _{x\to c}f(x)=\lim _{x\to c}g(x)=0\ }$

${\displaystyle \lim _{x\to c}f(x)=\lim _{x\to c}g(x)=\pm \infty }$

${\displaystyle \lim _{x\to c}h(x)=\lim _{x\to c}{\frac {f(x)}{g(x)}}=\lim _{x\to c}{\frac {f'(x)}{g'(x)}}}$

${\displaystyle {\begin{aligned}\lim _{x\to 0}{\frac {\sin x}{x}}&=\lim _{x\to 0}{\frac {\cos x}{1}}\\&=1\end{aligned}}}$

${\displaystyle {\begin{aligned}\lim _{x\to 0}{\frac {\ln x}{\frac {1}{x}}}&=\lim _{x\to 0}{\frac {\frac {1}{x}}{\frac {-1}{x^{2}}}}\\&=0\end{aligned}}}$