Prof. Alexandru Suciu
MTH 1125
Calculus 3
Spring 2002
SOLUTIONS TO QUIZ 7
(x 3)n
. For what values of x does the series converge absolutely,
n 3/ 4
n=1
converge conditionally, or diverge?
(a) Find the center of the series.
a=3
1. Consider the power series
Prof. Alexandru Suciu
MTH 1125
Calculus 3
Spring 2002
QUIZ 7
1. 8 points
Consider the power series
n=1
(x 3)n
n 3/4
For what values of x does the series converge absolutely, converge conditionally, or diverge?
Follow the steps below:
(a) Find the center o
Prof. Alexandru Suciu
MTH 1125
Calculus 3
Spring 2002
SOLUTIONS to QUIZ 3
1. 4 points You are given a formula for the nth term an of a sequence cfw_an . Find the values
a 1 , a 2 , a3 , a 4 .
(1)n+1
an = 2
n +1
1
a1 = ,
2
1
a2 = ,
5
a3 =
1
,
10
a4 =
1
17
Prof. Alexandru Suciu
MTH 1125
Calculus 3
Spring 2002
SOLUTIONS to QUIZ 4
1. 5 points Write down the rst 4 terms of the following series. Does the series
converge, or does it diverge? Find its sum if it converges. Explain!
n=1
2
3n
The series starts as:
n
Prof. Alexandru Suciu
MTH 1125
Calculus 3
Spring 2002
SOLUTIONS TO QUIZ 5
In each problem, decide whether the series converges or diverges. In either case, indicate which
test you are using, and justify your answer carefully.
Problem 1.
n=1
1
3n 1
Method
Prof. Alexandru Suciu
MTH 1125
Calculus 3
Spring 2002
QUIZ 6
1. 5 points Decide whether the following series converges absolutely, converges conditionally,
or diverges. Justify your answer.
1
(1)n
3
n
n=1
2. 5 points Decide whether the following series c
Prof. Alexandru Suciu
MTH 1125
Calculus 3
Spring 2002
QUIZ 5
1. 5 points Decide whether the following series converges or diverges. In either case, indicate
which test you are using, and justify your answer carefully.
n=1
1
3n 1
2. 5 points Decide whether
Prof. Alexandru Suciu
MTH 1125
Calculus 3
Spring 2002
QUIZ 1
1. 6 points
A particle moves along a line, with velocity v =
v = 1 + e2t ,
ds
dt
and initial position given by:
s(0) = 1
Find the particles position at time t.
2. 6 points A sailboat is running
Prof. Alexandru Suciu
MTH 1125
Calculus 3
Spring 2002
QUIZ 2
1. 6 points
Solve the dierential equation
dy
= x x ey/2 .
dx
[You may leave the solution(s) in implicit form.]
2. 6 points Use Eulers method to compute the rst two approximations (y1 and y2 ) to
Prof. Alexandru Suciu
MTH 1125
Calculus 3
Spring 2002
QUIZ 3
1. 4 points You are given a formula for the nth term an of a sequence cfw_an . Find the values
a 1 , a 2 , a3 , a 4 .
(1)n+1
an = 2
n +1
2. 4 points Does the following sequence converge, or does
Prof. Alexandru Suciu
MTH 1125
Calculus 3
Spring 2002
QUIZ 4
1. 5 points Write down the rst 4 terms of the following series. Does the series converge, or
does it diverge? Find its sum if it converges. Explain!
n=1
2
3n
2. 5 points Write down the rst 4 ter