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Unformatted text preview: MAT 1322 A Assignment 5 (Due Wed. April 1st at 8:30) 1. Starting from the Maclaurin series for
(ii) Student Number: 1
, ﬁnd the Maclaurin series of (i) ln(1 + x2 ) and
1−x ln(1 + x2 ) dx . For each, indicate on which open interval the series is guaranteed to be convergent and represent the given function.
Work: Answers: 2. Find the Maclaurin series of f (x) = (1 + x2 )1/3 .
Work: Answer: x2
4y 2
3. Sketch, on the same graph, the level curves of
−
= C for C = −1, 0, 1, 4 . Indicate the scale
4
9
on your axes and label the contours.
Answer: 4. Find all ﬁrst and second partial derivatives of the functions.
(a) f (x, y ) = 2x2 y 3 + 3x − ln(2)
Work: Answers: (b) g (r, θ) = r2 cos(3θ) − e3r (c) f (x, t) = ln x2 t − t
x ...
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This note was uploaded on 09/28/2011 for the course MATH 1322 taught by Professor Kousha during the Winter '10 term at University of Ottawa.
 Winter '10
 Kousha
 Maclaurin Series

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