MATH 1220 PRACTICE FINAL PLUS ADDITIONAL
QUESTIONS
MIKE WILLS
Practice Final
These are practice questions based on the material from the last
three sections of chapter 12. Be aware that the questions on the actual
final may be different in content from the questions here, but the level
of difficulty will be similar.
Problem 1. Write (1 + 3x)−4as a Taylor series. What is the radius
of convergence of your series?
Problem 2. Find the Maclaurin series for cos x.
Problem 3. Write the 5th order Taylor polynomial of sinh x.
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.
Problem 4. Find the first three non-zero terms in the Maclaurin series
for tan x.
Problem 5. For k∈Rand na non-negative integer, define the ex-
pression
(1) k
n.
Then write down the binomial series for (1 + x)kand state the radius
of convergence of the series. (Note that the radius of convergence will
depend on the value of k.)
Problem 6. Find the first four non-zero terms in the Maclaurin series
for exsin(2x).
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