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
work and write your answers inside your blue book. Put your test paper inside your blue book as
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
+
+ ··· + n + ···
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