3.6 L’Hospital’s Rule 罗比达法则 - 独中课程 | 线上补习

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3.6 L’Hospital’s Rule 罗比达法则

Evaluate the following limits
计算下列各极限

1. $\lim\limits_{x \to \infty}\frac{4^x}{4^x-1}$

2. $\lim\limits_{x\rightarrow\infty}\frac{e^x}{e^{2x}+e^{-x}}$

3. $\lim\limits_{x\rightarrow\pi}\frac{sin{x}}{x^2-\pi^2}$

$-\frac{1}{2\pi}$

4. $\lim\limits_{x\rightarrow0}\frac{1+sin{x}-cos{x}}{1-sin{x}-cos{x}}$

-1

5. $\lim\limits_{x\rightarrow\frac{\pi}{2}}(\frac{\pi}{2}-x)tan{x}$

6. $\lim\limits_{x\rightarrow \frac{\pi}{2}}(1+x)^{\frac{2}{x}}$

$e^2$

7. $\lim\limits_{x\rightarrow1}x^{1/(1-x)}$

$e^{-1}$

8. $\lim\limits_{x\rightarrow1}(ln{x})^{sin(x-1)}$

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