University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MATA37
Calculus II for Mathematical Sciences
Summer 2007
Assignment #9
This is the last assignment. Work on the text material and the problems below in preparation for
the the Final Exam, which takes place
Monday, August 13, 25pm, Room H215.
The last tutorial in on Tuesday, July 31. The quiz there will cover material on integration at your
TA’s discretion.
IMPORTANT NOTE!
Our course will end with Chapters 19. You only need to concern yourself
with problems 1  4 below. We will OMIT Chapters 20, 23 and 24 and you can therefore OMIT
problems 5  11 below.
PROBLEMS:
1. Page 377386
# 3(ix);
4(iii, x);
5(v);
6(ii, iv, v);
8(v, vi);
14;
23.
2. Determine the values of the real number
p
such that the improper integral
R
∞
1
1
x
p
dx
converges.
3. For each improper integral, determine whether it converges or diverges.
If the improper
integral converges, evaluate it.
(a)
R
∞
1
(3
x
+ 1)

2
dx
(b)
R

1
∞
(2

x
)

1
/
2
dx
(c)
R
∞
∞
xe

x
2
dx
(d)
R
∞
0
(
x
2
+ 3
x
+ 2)

1
dx
(e)
R
∞
∞
x
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 Winter '08
 Vadim
 Calculus, Limit of a sequence, improper integral converges, MCT

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