basic calculus

Math 150 Exam #4 NAME: M. Laurel Show all work, steps, and proper notation to insure full/partial credit. Use equal signs between each step. Lack of proper notation could result in point deductions. Show calculus work on all definite integrals or 0 points will be given. For problems 1-2, find each limit.

1. 0

arcsin lim

arctanx x x→

     

2. 2 9

lim xx x

e→∞  +    

For problems 3-12 evaluate each integral. Give exact answers for definite integrals

3. 22 7x

dx x −

∫

4. ln 8

0

xe dx∫

5. 1

2 0

30 4

dx x−

∫

6. 2

60 4 9

dx x+∫

7. 2 10

x x +∫ dx

8. 2100

x

x

e dx

e− ∫

9. 2

cos 25 sin

x dx

x+∫

10. 9

1 ln

e

e x x ∫ dx (change the limits of integration)

11. 2

arcsin 1

x dx

x− ∫

12. 2

1 x

dx x +∫

13. Use the 2nd derivative test to find the x-values where there are relative extreme points for the function ( ) xf x xe= .