Problem Set 8
Math 115, Fall 2016
1. Section 11.6:
8, 14, 20, 22
2. (a) For a series
an , show that 0 an + |an | 2|an |.
n=1
(b) Use part (a) and the comparison test to prove the absolute convergence theorem.
That is, show that if
|an | converges, then
an
Problem Set 3
Math 115, Fall 2016
1. Section 6.2:
18, 24, 56
2. The circumference of a tree trunk at dierent heights above the ground is given in the
table below. Assume that all horizontal cross-sections of the tree are circles. Estimate
the volume of th
Problem Set 5
Math 115, Fall 2016
1. Section 7.8:
2, 16, 20, 30, 54
2. (a) Find ann upper bound for
Z
2
e x d x
3
2
using the fact that e x e 3x for x 3.
(b) For any positive n, generalize the result of part (a) to find an upper bound for
Z
2
e x d x
n
by
Problem Set 6
Math 115, Fall 2016
1. Section 11.1:
14, 24, 36, 42, 50
2. (a) Cans are stacked in a triangle on a shelf. The bottom row contains k cans, the row
above contains one fewer can, and so on, until the top row, which has one can. How
many rows ar
Problem Set 1
Math 115, Fall 2016
1. Section 5.1:
2, 16, 22
2. A woman drives 10 miles, accelerating uniformly from rest to 60 mph. Graph her velocity
versus time. How long does it take for her to reach 60 mph?
3. Section 5.2:
10, 48, 58
4. Sketch the gra
Problem Set 4
Math 115, Fall 2016
1. Section 7.5: 18, 22, 64, 66
Z 10
2. Estimate
f (x)g 0 (x) d x if f (x) = x 2 and g has the values in the following table.
0
x
g(x)
3. Section 7.7:
0
2.3
2
3.1
4
4.1
6
5.5
8
5.9
10
6.1
2, 20, 22, 46
1
Problem Set 2
Math 115, Fall 2016
1. Section 5.3:
4, 10, 30, 62
2. A car speeds up at a constant rate from 10 to 70 mph over a period of half an hour. Its
fuel efficiency (in miles per gallon) increases with speed; values are in the table below.
Make lowe
Problem Set 7
Math 115, Fall 2016
1. Section 11.3:
6, 12, 32
2. Section 11.4:
12, 24, 30
3. Suppose 0 b n 2n an and 0 cn 2n d n for all n. Which of the following series
definitely converge and which definitely diverge:
n=1
an ,
n=1
bn ,
n=1
cn ,
dn
n=1
An