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.
Answer :
1
2. ![Rendered by QuickLaTeX.com \lim\limits_{x\rightarrow\infty}\frac{e^x}{e^{2x}+e^{-x}}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-ac2b5cf2a8e199c5f74d4bcd343bf20c_l3.png)
![Rendered by QuickLaTeX.com \lim\limits_{x\rightarrow\infty}\frac{e^x}{e^{2x}+e^{-x}}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-ac2b5cf2a8e199c5f74d4bcd343bf20c_l3.png)
Answer :
0
3. ![Rendered by QuickLaTeX.com \lim\limits_{x\rightarrow\pi}\frac{sin{x}}{x^2-\pi^2}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-0ffdd1fd0a6a52e8fa5e5cf403129b3f_l3.png)
![Rendered by QuickLaTeX.com \lim\limits_{x\rightarrow\pi}\frac{sin{x}}{x^2-\pi^2}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-0ffdd1fd0a6a52e8fa5e5cf403129b3f_l3.png)
Answer :
![Rendered by QuickLaTeX.com -\frac{1}{2\pi}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-0b8855e927456bebfc57503f3e1162a8_l3.png)
4. ![Rendered by QuickLaTeX.com \lim\limits_{x\rightarrow0}\frac{1+sin{x}-cos{x}}{1-sin{x}-cos{x}}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-2d6aabdd6ebbf79b9ff4ef62040fef4f_l3.png)
![Rendered by QuickLaTeX.com \lim\limits_{x\rightarrow0}\frac{1+sin{x}-cos{x}}{1-sin{x}-cos{x}}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-2d6aabdd6ebbf79b9ff4ef62040fef4f_l3.png)
Answer :
-1
5. ![Rendered by QuickLaTeX.com \lim\limits_{x\rightarrow\frac{\pi}{2}}(\frac{\pi}{2}-x)tan{x}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-895fe399879aede9e17d742d8b046dba_l3.png)
![Rendered by QuickLaTeX.com \lim\limits_{x\rightarrow\frac{\pi}{2}}(\frac{\pi}{2}-x)tan{x}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-895fe399879aede9e17d742d8b046dba_l3.png)
Answer :
1
6. ![Rendered by QuickLaTeX.com \lim\limits_{x\rightarrow \frac{\pi}{2}}(1+x)^{\frac{2}{x}}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-0983c3ebd058fb9b8ebc784d08483590_l3.png)
![Rendered by QuickLaTeX.com \lim\limits_{x\rightarrow \frac{\pi}{2}}(1+x)^{\frac{2}{x}}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-0983c3ebd058fb9b8ebc784d08483590_l3.png)
Answer :
![Rendered by QuickLaTeX.com e^2](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-7a003b37e015196477b8eea35e58522e_l3.png)
7. ![Rendered by QuickLaTeX.com \lim\limits_{x\rightarrow1}x^{1/(1-x)}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-52f23965f46d2e01aed45a6ccc0f6f20_l3.png)
![Rendered by QuickLaTeX.com \lim\limits_{x\rightarrow1}x^{1/(1-x)}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-52f23965f46d2e01aed45a6ccc0f6f20_l3.png)
Answer :
![Rendered by QuickLaTeX.com e^{-1}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-92677d1bfa09d59be588ac7501067ab9_l3.png)
8. ![Rendered by QuickLaTeX.com \lim\limits_{x\rightarrow1}(ln{x})^{sin(x-1)}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-3295042f94bbd391c8715ae4854b82ff_l3.png)
![Rendered by QuickLaTeX.com \lim\limits_{x\rightarrow1}(ln{x})^{sin(x-1)}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-3295042f94bbd391c8715ae4854b82ff_l3.png)
Answer :
1