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University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MATA37
Calculus II for Mathematical Sciences
Summer 2007
Assignment #3
Work on the text and lecture material and the problems below in preparation for your 3rd tutorial
which takes place during the week of May 28  June 1.
Remember:
you will have a quiz on
assignment 2 in your 3rd tutorial also.
The quiz on assignment 3 is in your 4th tutorial which takes place during the week of June 48.
STUDY:
Chapters 5 and 6 for this assignment. Chapters 79 for the nearfuture lectures.
PROBLEMS:
1. Page 117119 # 5, 6, 13, 16(ac).
2. Assume
f
is continuous on
R
. If
f
(
c
)
<
0 for some
c
∈
R
, prove there exists an open interval
(
a,b
) containing
c
such that
f
(
x
)
<
0 for all
x
∈
(
a,b
). Formulate an analogous statement if
f is positive at
c
.
3. Assume
h
is continuous on
R
. Give any point
c
∈
R
, show there exists a number
K
≥
0 and
numbers
a < b
such that

h
(
x
)
 ≤
K
for all
x
∈
[
a,b
].
4. Let
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This note was uploaded on 10/28/2010 for the course MATHEMATIC MATA37 taught by Professor Vadim during the Winter '08 term at University of Toronto.
 Winter '08
 Vadim
 Calculus

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