# Math 141 Final Exam

## Math 141/6380, Due by 11:59pm, Sunday, March 4, 2018

This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. You must complete the exam individually. Neither collaboration nor consultation with others is allowed.

Suggestions about how to approach this Final Exam:

1. Print out a copy of the Final Exam and solve any problems that you can using pencil and paper.
2. Review the eBook sections associated with any problems you could not solve.
3. Complete the remaining problems to the best of your ability. Even if you cannot come to a final solution, you should show me what you do know so that you have the opportunity for partial credit.
4. Review your work. Check for errors. Make sure you have included units where appropriate, and explanations when required by the instructions.
5. When you are satisfied, type in your solutions (extend space if needed) or, if you have the facilities, you can scan your hand written work or take photos with your camera. Make sure that your submission is readable.
6. Submit your work in the associated LEO assignment.

Unless the problem explicitly states otherwise, work must be shown for every answer. Any answer, even if “correct” but lacking work, will NOT receive full credit and may receive NO credit!

Please submit the exam as an attachment in any readable formats such as scanned or photo copy before or on Sunday, March 4. No late exam will be accepted. No make-up final exam will be arranged. Solution keys for the Final Exam will NOT be released.

 . Please sign (or type) your name below the following honor pledge: I have completed this exam by myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this exam. Name ___________ Date_________

# Math 141 Final Exam

## Math 141/6380, Dr. Chiang, Due by 11:59PM, Sunday

NAME: _________SCORE: 250 Points

(An answer, even if “correct” but lacking work, will NOT receive full credit!)

1. Evaluate each integral by making an appropriate substitution.

(a)

(b)

(c)

2. Find the area of the region bounded above by the graph of and below by the graph of.

3. Let R be the closed region between the graphs of and on the interval [0, 1]. Find the volume V of the solid obtained by revolving R about the x axis.

4. Let R be the closed region between the graphs of and on the interval [0, 1]. Find the volume V of the solid obtained by revolving R about the y axis. (Same graph as for Problem3)

5. Find the length of arc on the graph of

from to

6. Find the area of the surface generated by revolving about the x-axis the curve on .

7. Fill in the values of and for . Provide detail to support your answers.

 x 1 2 5 2 3 3 1 3

8. Calculate the derivative for

9. Use the definition of an improper integral to evaluate the following integrals. If an integral converges, evaluate its value.

(a)

(b)

10. Using the indicated techniques to evaluate the following integrals. Show work detail to support your solutions. Solving using other methods or with no detail is not acceptable.

(a) (Trigonometric substitution)

(b) (Trigonometric substitution)

(c) (Integration by Parts)

11. Complete the square in the denominator, make appropriate substitution, and integrate.

12. Find the partial fraction decomposition for the rational function and then evaluate the integral

13. State whether the sequence converges or diverges. If it converges, find its limit.

14. Using the Integral Test to test the following series for convergence. Solving using other methods or with no detail is not acceptable.

15. Determine whether the following series converge or diverge. Indicate the test you use.

(a)

(b)

16. Determine whether the series converges or diverges. If it converges, find its sum.

17. Determine whether the series converges conditionally, or converges absolutely, or diverges and give reasons for your conclusions.

18. Find the interval of convergence for the power series

19. Use substitution method and a known power series to find power series for . Please express your answer in one sigma notation.

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