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Midterm

MATH 141 McGill Examf98Exam


Department
Mathematics and Statistics
Course Code
MATH 141
Professor
All
Study Guide
Midterm

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Math 106C Name
Final Exam Version 1
12/16/15
Read directions carefully and show all your work. Partial credit will be assigned based upon the correctness,
completeness, and clarity of your answers. Correct answers without proper justification or those that use un-
approved short-cut methods will not receive full credit. If you use a calculator to help find an answer, you
must write down enough information on what you have done to make your method understandable. Give exact
answers unless otherwise noted.
1. (20 pts.) Evaluate the following integrals.
(a) Ze2xexdx
(b) Zsin2xcos3x dx
(c) Zarctan x dx
1

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(d) Zx
(1 + x2)3/2dx
2. (8 pts.) The Maclaurin series for ln(1 + t) =
X
k=1
(1)k+1tk
kon (1,1). Find the first four non-zero terms
of the Maclaurin series for f(x) = ln(1 + 2x)
x.
2

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3. (8 pts.) Find the interval of convergence for the series
X
k=1
3(2x3)k
k·7k.
4. (8 pts.) Solve the initial value problem dy
dx =x2+ 2
3y2with y(0) = 2.
3
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