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# L'Hopital's Rule, Integrals & Series in Calculus Chapter Exam

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

### Page 1

#### Question 1 1. Evaluate and solve the following integral.

#### Question 2 2. Evaluate the limit shown below:

####
Question 3
3.
Evaluate the limit shown below:

(Hint: You can use L'Hopitals's Rule more than once!)

#### Question 4 4. Evaluate and solve the following integral.

#### Question 5 5. What is the limit of the following:

### Page 2

#### Question 6 6. Evaluate the limit of the following:

#### Question 7 7. A ball is dropped and begins bouncing. On the first bounce, the ball travels 3 feet. Each consecutive bounce is 1/8 the distance of the previous bounce. What is the total distance that the ball travels after it first hits the ground? Round to the nearest hundredth.

#### Question 8 8. Find the following limit:

#### Question 9 9. Of the three limits shown below, which can be evaluated using L'Hopital's Rule?

#### Question 10 10. Find the sum of the following geometric series:

### Page 3

#### Question 11 11. Find the following limit:

#### Question 12 12. Find the following limit:

#### Question 13 13. Evaluate and solve the following integral.

#### Question 14 14. Does L'Hopital's rule apply to this problem? Why or why not?

#### Question 15 15. Evaluate and solve the following integral.

### Page 4

#### Question 16 16. Find the following limit:

#### Question 17 17. Evaluate the limit shown below:

#### Question 18 18. Evaluate and solve the following integral.

#### Question 19 19. Evaluate the limit shown below:

####
Question 20
20.
According to L'Hopital's rule, which of the following statements MUST be true for the equation shown below to hold?

A) f(x) and g(x) approach 0 or infinity

B) f'(C) does not equal 0

C) g'(x) does not equal 0

### Page 5

#### Question 21 21. Find the sum of the following geometric series:

#### Question 22 22. Find the following limit:

#### Question 23 23. Use L'Hopital's rule to evaluate the limit

#### L'Hopital's Rule, Integrals & Series in Calculus Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!