University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MATA37
Calculus II for Mathematical Sciences
Summer 2007
Assignment #5
Work on the text material and the problems below in preparation for your 5th tutorial on Tuesday,
June 12. Remember that there is a quiz on assignment 4 in that tutorial.
The quiz on assignment 5 is in your 6th tutorial which is on Tuesday, June 19. This is the week of
our Midterm Test (which is on Saturday, June 23, 24pm, in room H215).
STUDY:
Chapters 89 for this assignment. Chapters 1011 for future assignments and lectures.
PROBLEMS:
1. Page 129
# 17,
18(a).
2. Page 137
# 1(viii),
2(a) (What is this problem really about?).
3. Let
A
and
B
be nonempty, bounded subsets of
R
.
Define
AB
=
{
ab
:
a
∈
A, b
∈
B
}
.
Determine with proof whether
inf
(
AB
) =
inf
(
A
)
inf
(
B
).
4. Page 161 #
1,
2,
3,
14,
15(a).
5. Define a function
f
on all of
R
by
f
(
x
) =
x
2
if
x
is rational and
f
(
x
) =

x
2
if
x
is irrational.
Draw a good picture of the graph of
y
=
f
(
x
). Determine with proof the points where
f
is
differentiable.
6. Use the definition of derivative to calculate
f
0
(
x
) for the function
f
(
x
) =
x
1
/
3
. Compare the
domain of
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 Winter '08
 Vadim
 Calculus, mathematical sciences, Scarborough Department of Computer and Mathematical Sciences, Sciences MATA37 Calculus, Mathematical Sciences Summer

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