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McGILL UNIVERSITY
FACULTY OF SCIENCE
FINAL EXAMINATION
MATHEMATICS 262
Examiner: Professor Jakobson
Date: Thursday, December 9, 2004
Associate Examiner: Professor Jaksic
Time: 14:00 A.M.  17:00
INSTRUCTIONS
Answer all seven questions. Each question is worth 10 points. Please
give a detailed explanation for each answer.
Nonprogrammable calculators are permitted.
This is a closedbook exam
This exam comprises the cover and two pages of questions.
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View Full DocumentMATH 262: FINAL EXAM
page 1
Problem 1. (10 points)
Consider power series
∞
X
n
=2
(

1)
n
x
n
n
(
n

1)
.
a) [2 pts] Find the radius of the convergence of the power series.
b) [2 pts] Find the interval of convergence of the power series.
c) [2 pts] Find the second derivative of the power series.
d) [4 pts] Find the sum of the original power series.
Problem 2. (10 points)
Consider the circular helix
r
(
t
) = 3 cos
t
i
+ 3sin
t
j
+ 4
t
k
.
a) [3 pts] Parametrize
r
in terms of the arc length
r
(
s
) measured from the point
(1
,
0
,
0) in the direction of increasing
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 Math, Calculus

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