calculus

Midterm 02

Course Code: 021 Course Name: Calculus II

Student Name: Date: 20 July 2020

Total Score: 100

Obtained Score:

Time: 9am to 10:30am

Note:

1. All students need to download this Midterm, after solving the required

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

system.

2. Only hand written solutions are acceptable.

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

all.

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

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

Solve the entire questions:

Question 01: (10)

Evaluate the following Integral:

Question 02: (10)

Find the sum of the series.

Question 03: (15)

How we can use these three methods to solve mathematical problems

give example for each method.

 Integration by Parts

 Improper Integrals

 The Integral Test

Question 04: (10)

Find n for the series in which a1= 5, d = 3, Sn =330

Question 05: (20)

Evaluate:

1)

2)

Question 06: (10)

For what values of r is the sequence { r n } convergent?

Question 07: (15)

Integrate by using trigonometric substitution.

1)

2)

Question 08: (10)

Integrate the following:

4 sec 3x dx