Math 252 Online Graded Assignment #2

It is essential to show all steps by hand. Also, if a method is prescribed, use only that method (no credit otherwise.)

Answers must be exact. Decimal approximations may not be given unless they are asked for

1a. (4 points) Determine the integral by u-substitution.

1b. (8 points) Determine the integral .

2a. (4 points) Determine the integral by u-substitution.

2b. (8 points) Determine the integral by completing the square in the denominator.

3a. (4 points) Determine the integral by u-substitution.

3b. (8 points) Determine the integral .

4a. (4 points) Determine the integral by u-substitution.

4b. (8 points) Determine the integral .

4c. (8 points) Determine the integral .

5. (8 points) Determine the integral .

6a. (4 points) Determine the integral dx by u-substitution.

6b. (8 points) Determine the integral dx .

7. (8 points) Determine the integral dx .

8. (8 points) Justifying its use, use L’Hôpital’s Rule to evaluate the following limit.

9. (8 points) Determine whether converges or diverges. Evaluate the integral if it converges.