University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MATA37
Calculus II for Mathematical Sciences
Summer 2007
Assignment #4
Work on the text material and the problems below in preparation for your 4th tutorial, which takes
place during the week of June 4  8.
Remember:
there is a quiz on Assignment 3 in that tutorial.
The quiz on Assignment 4 takes place in the 5th tutorial which is during the week of June 11  15.
STUDY:
Chapters 68 for this assignment and Chapters 911 for the nearfuture lectures.
PROBLEMS:
1. Page 118119
# 7;
10 (b).
2. Page 127130
# 1 (i,
iii);
3;
8;
10;
14 (a, b);
19 (a).
3. Page 137139
# 1 (i,
iii,
iv);
12;
13.
4. Assume
φ
is continuous on a closed, bounded interval [
a, b
]. The image of [
a, b
] under
φ
is the
set
φ
([
a, b
]) =
{
φ
(
x
)

x
∈
[
a, b
]
}
. Prove that
φ
([
a, b
]) is a closed, bounded interval.
5. Give an example of a function
ψ
and a bounded, open interval (
a, b
) such that
ψ
is continuous
on (
a, b
) but
ψ
((
a, b
)) is an unbounded, open interval. Give an example of a function
ψ
that
is continuous on
R
but for which
ψ
(
R
) is a bounded, open interval.
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 Winter '08
 Vadim
 Calculus, Topology, Metric space, nonempty subset, Scarborough Department of Computer and Mathematical Sciences

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