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.

arcsin limx arctan

x

→ x

2.

2 9 lim x x

x

→∞ e

+

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

3.

2 2 7 x dx

x

− ∫

4.

ln8

x e dx ∫

5.

1

2

30

4

dx − x

∫

6. 2

60

4 9

dx

+ x ∫

7. 2 10

x

x + ∫ dx

8. 2 100

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 ( ) x f x xe = .