We've updated our
Privacy Policy effective December 15. Please read our updated Privacy Policy and tap

TEXT

Advanced L'Hopital Rule Worksheets

Limits

Advanced

L'Hopital Rule

1. \lim _{x\to \infty}(\frac{\ln(x)}{x})

1. \lim _{x\to \infty}(\frac{\ln(x)}{x})

2. \lim _{x\to -\infty}(xe^x)

2. \lim _{x\to -\infty}(xe^x)

3. \lim _{x\to 0}(\frac{sin(x)}{x})

3. \lim _{x\to 0}(\frac{sin(x)}{x})

4. \lim _{x\to 0}(\frac{\tan(x)}{2x})

4. \lim _{x\to 0}(\frac{\tan(x)}{2x})

5. \lim _{x\to 0}(\frac{1-\sec^{2}(7x)}{(3x)^{2}})

5. \lim _{x\to 0}(\frac{1-\sec^{2}(7x)}{(3x)^{2}})

6. \lim _{x\to 0}(x\ln (x))

6. \lim _{x\to 0}(x\ln (x))

7. \lim _{x\to 0}(\frac{\sin(5x)}{\sin(3x)})

7. \lim _{x\to 0}(\frac{\sin(5x)}{\sin(3x)})

8. \lim _{x\to \infty}(\frac{e^x}{x^2})

8. \lim _{x\to \infty}(\frac{e^x}{x^2})

9. \lim _{x\to 0}(\frac{\sin(5x)}{2x})

9. \lim _{x\to 0}(\frac{\sin(5x)}{2x})

10. \lim _{x\to 0}(\frac{1-\cos(2x)}{x})

10. \lim _{x\to 0}(\frac{1-\cos(2x)}{x})

Answers

Limits

Advanced

L'Hopital Rule

1. 0

2. 0

3. 1

4. \frac{1}{2}

5. -\frac{49}{9}

6. \mathrm{Does\:not\:exist}

7. \frac{5}{3}

8. \infty

9. \frac{5}{2}

10. 0