calculus II

Final Exam

Course Code: 021 Course Name: Calculus II

Total Score: 100 Class Time: 9:00 to 10:30

Obtained Score:

Student Name:

Date: August 4, 2020

Instructions:

1. Check the condition of the test questionnaire booklet before you answer, and

request for an immediate replacement if there is any missing page or printing

problem.

2. All students need to download this Final Exam, after solving the required

questions you need to scan it and make a pdf file then upload into the system.

3. Only hand written solutions are acceptable.

4. Uploading Pictures with mobile phone without pdf file is not acceptable at all.

5. Solve each question below by showing all the necessary steps.

6. This is CLOSED BOOK examination. Mobile phones and any other electronic

devices can’t be used.

7. NO MAKEUP EXAM WILL BE GIVEN.

8. If still you have any problem you can ask me via e-mail.

I hereby certify that I have read and understood the examination policy. Affix is my

signature as I conform to the said rules.

Signature of Student: _______________

Best of Luck

Solve the entire questions:

Question 01: (10)

Find the volume of the solid of revolution formed by rotating the finite

region bounded by the graphs of and about

the y-axis.

Question 02: (15)

a) If a > 0 find the area of the surface generated by rotating the

loop of the curve about the x-axis.

b) Find the surface area if the loop rotated about the y-axis.

Question 03: (10)

Find the estimating sum of this infinite series for K=4.

Question 04: (15)

Evaluate the following Integral:

a)

b)

c)

Question 05: (10)

a) Evaluate:

b) Find the Maclaurin series for and prove that it represents

for all x.

Question 06: (15)

a) Solve by using Ratio test

b) Solve with the help of limit comparison test

c) Solve with the help of integral test

Question 07: (10)

a. Sketch the curve with polar equation

r = 1+ cos θ.

b. Find a Cartesian equation for this curve

Question 08: (15)

a) Graph the curve r = 5 and θ = π/4.

b) Represent the point with Cartesian coordinates (2, 2), (1, - ),

(-1, ) in terms of polar coordinates.

c) Convert the point (2, π/4) and (3, -π/3) from polar to Cartesian

coordinates.