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 = .
