Course Content
第4章:坐标变换
高三数学 | 高级数学
About Lesson
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}

Answer :
1
2. \lim\limits_{x\rightarrow\infty}\frac{e^x}{e^{2x}+e^{-x}}
Answer :
0
3. \lim\limits_{x\rightarrow\pi}\frac{sin{x}}{x^2-\pi^2}
Answer :
-\frac{1}{2\pi}
4. \lim\limits_{x\rightarrow0}\frac{1+sin{x}-cos{x}}{1-sin{x}-cos{x}}
Answer :
-1
5. \lim\limits_{x\rightarrow\frac{\pi}{2}}(\frac{\pi}{2}-x)tan{x}
Answer :
1
6. \lim\limits_{x\rightarrow \frac{\pi}{2}}(1+x)^{\frac{2}{x}}
Answer :
e^2
7. \lim\limits_{x\rightarrow1}x^{1/(1-x)}
Answer :
e^{-1}
8. \lim\limits_{x\rightarrow1}(ln{x})^{sin(x-1)}
Answer :
1
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