MATH 1220 PRACTICE MIDTERM 3 PLUS
ADDITIONAL QUESTIONS
MIKE WILLS
Practice Midterm
This is a practice midterm. Try to time yourself on it. Be aware
that the questions on the actual midterm may be different in content
from the questions here, but the level of difficulty will be similar. I will
type up solutions at a later date.
Problem 1. Find the area of the region in the xy-plane bounded by
θ= 0, θ=π
2, and r=e2θwhere rand θare the usual polar coordinates.
Problem 2. Define the following terms:
(i) bounded sequence
(ii) monotonic sequence
State the monotonic sequence theorem.
Problem 3. Consider the series
∞
X
n=1
(−1)n3n−2
4n+ 5. Is it divergent, con-
ditionally convergent, or absolutely convergent?
Problem 4. Give two examples to illustrate why the ratio test is in-
conclusive when R= 1.
Problem 5. What is the interval of convergence of the power series
∞
X
n=1
xn
n?
Problem 6. Compute R1
0ex3dx. You may assume that eu=
∞
X
n=0
un
n!
for all u∈R.
Additional Problems
I will not type up solutions for these problems. I include them so
that you can get a better feel for the type of questions that I am likely
to ask.
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