Math 126-103 (CRN 12418)
Fall 2014
Test 2
Carter
General Instructions. Write your name on only the outside of your blue books. Do not write on
this test sheet, do all of your work inside your blue books. Write neat complete solutions to each of
the problems in the blue book. Please put your test sheet inside the blue book as you leave. There
are 105 points.
Fusion food suggestion: Kung pao tacos.
1. Compute the following integrals (8 points each):
(a)
Z
dx
dx
(x + 2)(x − 3)
(b)
∞
Z
2
(c)
√
Z
√
dx
x(ln(x))2
3/2 p
1 − x2 dx
2/2
(d)
Z
sin3 (2x) dx
(e)
Z
arcsin (x) dx
2. Determine the limit of the sequences (5 points each):
(a)
an =
(−1)n
n
(b)
an =
3n2
n−2
+ 6n + 8
(c)
an = (0.15)n
(d)
1 n
an = 1 +
n
(e)
an =
2n
n!
3. Give a formula for the nth partial sum of the series and use this formula to sum the series
(10 points):
∞ X
1
1
−
k (k + 1)
k=1
4. Sum the geometric series (10 points):
n
2 3
∞ k
X
1
1
1
1
1
+
+
+ ··· +
+ ··· =
4
4
4
4
4
k=1
5. Use any test that you like to determine if the given series converges (5 points each):
(a)
∞
X
n=2
1
n (ln (n))2
(b)
∞
X
2n
n=1
n!
(c)
∞
X
n=1
1
n101/100
(d)
∞ X
1 n
1+
n
n=1