微積分上課筆記5

段考範圍

羅畢達定理

when $f(x)$ and $g(x)$ are differentiable and $g’(a)\neq 0$,then
if $\displaystyle \lim_{x \rightarrow a} f(x) = 0$ $\displaystyle \lim_{x \rightarrow a} g(x) = 0$ (or equal to $\displaystyle +-\infty$),then
$\displaystyle \lim_{x \rightarrow a} \frac{f(x)}{g(x)} = \lim_{x \rightarrow a} \frac{f’(x)}{g’(x)}$
while $\displaystyle \color{red} \lim_{x \rightarrow a} \frac{f(x)}{g(x)}$ exists

適用條件

1. $\frac{0}{0}$ or $\frac{\infty}{\infty}$
2. $0$ or $\infty$
3. $\infty - \infty$
4. $0^\infty$,$\infty ^ 0$ and $1 ^ \infty$