School

McGill UniversityDepartment

Mathematics and StatisticsCourse Code

MATH 141Professor

AllStudy Guide

MidtermThis

**preview**shows pages 1-3. to view the full**10 pages of the document.**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

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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.

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3. (8 pts.) Find the interval of convergence for the series

∞

X

k=1

3(2x−3)k

k·7k.

4. (8 pts.) Solve the initial value problem dy

dx =x2+ 2

3y2with y(0) = 2.

3

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