# Math 126-104 Test 2 Spring 2013 Carter

```Math 126-104
Test 2
Spring 2013
Carter
General Instructions: Write your name on only the outside of your blue book. Do all of your
you leave. Solve each of the following problems; point values are indicated on the problems. There
are 114 total points available on the test. Try a fresh apple for dessert.
Compute the following (10 points each).
1.
Z
2.
e2x sin e2x dx
Z
arcsin x dx
3.
4
Z
(16 − x2 )1/2 dx
0
4.
Z
5.
1
dx
(x + 2)(x − 1)
Z
∞
dx
ex
0
6. For the recursively defined sequence, write out the first 5 terms. If possible, give a closed
formula for the general term, and determine if the sequence converges (15 points).
a1 = 1,
an+1 = an + (1/3n ) .
7. Determine the limit of the sequence (10 points).:
an =
sin n
n
8. Determine a formula for the nth partial sum and sum the series (10 points):
1+
1
1
1
+
+ &middot;&middot;&middot; + n + &middot;&middot;&middot;
8 64
8
9. Use any test that you like to determine if the given series converges (10 points each).
(a)
∞
X
n=2
√
1
n ln n
(b)
∞
X
n=1
n2
1
+n
```