University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MATA37
Calculus II for Mathematical Sciences
Summer 2007
Assignment #7
Work on the text material and the problems below in preparation for your tutorial on Tuesday,
July 17. You will have a quiz on this assignment 7 (only up to and including Chapter 11) or any of
the material covered in assignment 6.
STUDY:
Chapters 11, 13, 14, and 19 for this assignment. Omit Chapters 12, 1315, and 18.
We will not rigorously cover the theory of integration in Chapter 13, but you should read through
that material a few times anyway.
It may also be useful to read about integration in Stewart’s
Calculus book (as used in MATA30). Chapters 5  7 are appropriate there too. In Spivak’s book,
study Newton’s method on page 457 and in Stewart’s book read through Section 4.9.
PROBLEMS:
1. Page 202212
# 4(a),
19,
26,
27,
32,
37,
41,
44,
49,
50,
60.
2. Let
I
be an interval.
If a differentiable function
f
is strictly increasing on
I
◦
, prove that
f
0
(
x
)
≥
0 for all
x
∈
I
◦
. Show by an example that we cannot generally replace
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 Winter '08
 Vadim
 Calculus, Mathematical Sciences Assignment

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