# Walden Calculus Coronavirus Edition Questions

Description

2. Find the slope of the tangent line to the polar curve r
cos 2
when
3
1
3. Use the integral test to determine if
n 2
n ln n
2
is convergent or divergent. Explain
x 1
4. Find the radius of convergence of
n 3
5n n
n
5. Use one of your comparison tests to decide if
n
n 1
converges. Justify your
2n 2 7
3 n
6
6. Find the area of the shaded region of the graph of r 1 sin
an , sn is the n th partial sum of s , and the terms of the series
7.(24 pts) Suppose S
n 1
n 1
are defined by an
2 3
5n
. (a. and b. are 5 points each, c. and d. are 7 points each)
a. Write out the first 3 terms of the sequence an (you don’t need to simplify your work).
a1
a2
a3
b. Write out the first 4 terms of the sequence sn (you don’t need to simplify your work).
s1
s3
s2
s4
c. Determine if the sequence an converges or diverges. If it converges, find the limit.
d. Determine if the series S converges or diverges. If it converges, find the limit.
x2
8. (5 points each) The figure below shows the graphs of f x 2 x , and g x
.
4
Also shown are regions R1 , R2, and R3. Use the figure to answer the following questions.
In each case set-up your integral answer but do not evaluate it.
a. Set up the integral or integrals to find
the area of the region R2.
b.
Set up the integral or integrals needed to find the volume formed by rotating R1
the y-axis.
c. Set up the integral or integrals needed to find the volume formed by rotating R2 .about
the x-axis.
8) For work with sequences and series
i) For showing the convergence or divergence of a sequence show the
steps you used to find the limit. Then state your conclusion.
ii) If you are finding the sum of a geometric series,
ar n 1 or
n 1
ar n , make
n 0
sure you show how you found the value of a and r .
iii) For testing the convergence or divergence of a series
i) Name the test you are using and explain how your results from using
ii) For a geometric series make sure you show the value of r and explain
what that means for the convergence of the series.
9) You may print a copy of the test and do your work on it or copy and do the
problems, in order, on notebook paper. I want at most two problems on
one letter size sheet of paper. Space your work out so I can comment if
needed. You should have plenty of room to show your work. Do not cramp
it so I can follow your thinking on the problem. Some problems will be very
short. Others may take a lot of space. That is fine. Two problems at most
per side of paper!
10)Make sure what you write is readable on the pdf you upload! Write neatly
using a pencil or pen that is dark enough to show up well on the scanned
pdf. When you scan your exam, lighting is important. Check your scanned
test to verify that it is complete and legible before you upload it to
Canvas.
11)When you scan your work make sure your scanner is in “batch mode”. That
way I get one pdf file not a separate file for each page. The pages should be
the same order as the pdf test document.
12)Late work is penalized at 10% ( a letter grade ) per day.