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Math 1ZZ5
1st Sample Test #2
Name
:___________________________________________
(Last Name)
(First Name)
Student Number:
Tutorial Number:
_____________________
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This test consists of 13 multiple choice questions worth 1 mark each (no part marks), and 1
question worth 1 mark (no part marks) on proper computer card filling.
All questions must be
answered on the COMPUTER CARD with an HB PENCIL.
Marks will not be deducted for
wrong answers (i.e., there is no penalty for guessing).
You are responsible for ensuring that your
copy of the test is complete.
Bring any discrepancy to the attention of the invigilator.
Calculators are NOT allowed.
1.
Write out the form of the partial fraction decomposition of the following function
B&B%B$B#
B ÐB"ÑÐB *Ñ
%$#
$#
#
.
(a)
EF G
B
H
B
B"
ÐB *Ñ
#
(b)
E
F
GBH
IBJ
B
B"
B*
ÐB*
Ñ
#
#
(c)
EFG
H
I
J
B
B
B
Ñ
#$
#
#
#
(d)
E
F
G
H
IBJ
KBL
B
B
B
Ñ
#
#
#
(e)
EF
G
B
B"
ÐB *Ñ
#
2.
Evaluate the following improper integral.
∞
!
%B
B/ .B
&
(a)
(b)
(c)
(d)
(e)
Divergent
"!
""
%&
3.
Using the comparison theorem, which of the following integrals is convergent?
(i)
"
∞
BB
"B
sin
#
$
(
.B
(ii)
"
∞
B/
#B
(iii)
#
∞
B
#
'
(a)
(b)
(c)
(d)
(e)
(i) only
(ii) only
(i) and (ii) only
(i) and (iii) only
(ii) and (iii) only
4.
Evaluate the following integral.
B*
B $B"!
#
(a)
(b)
ln
ln
ln
ln
lB&l# lB#l
# lB&l lB#l
(c)
(d)
ln
ln
ln
ln
lB&l# lB#l
lB&l# lB#l
(e)
# lB&l lB#l
ln
ln
5.
Perform the following division:
B#B&
BB'
$
#
(a)
(b)
(c)
B"
&B""
B B'
&B""
B"
B"
B B'
B B'
&B""
#
##
(d)
(e)
B "
$B "
$B"
B"
B B'
B B'
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View Full Document 6.
Find the values of
for which the series is convergent.
:
8œ#
∞
:"
Ð8
Ñ
8
ln
(a)
(b)
(c)
(d)
(e)
: "
:!
:Ÿ!
:"
:Ÿ"
7.
If we use the partial sum
to approximate the sum of the series
=
"!
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This note was uploaded on 04/04/2011 for the course MATH 1zz5 taught by Professor Child during the Spring '10 term at McMaster University.
 Spring '10
 Child
 Math

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