Math 1ZB3
1st Sample Test #3
Name
:___________________________________________
(Last Name)
(First Name)
Student Number:
Tutorial Number:
_____________________
____________________
This test consists of 14 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.
Find the values of
for which the series is convergent.
:
8œ#
∞
:"
Ð
8Ñ
8
ln
(a)
(b)
(c)
(d)
(e)
: "
: !
: Ÿ !
: "
: Ÿ "
2.
If we use the partial sum
to approximate the sum of the series
=
"!
8œ"
∞
%
"
8
estimate the error involved in the approximation.
"
"
"
"
"
$!!!
&!!!
"!!!!
"!!!
"%'%"
3.
Find the length of the curve
for
.
C œ
B
" B
! Ÿ B Ÿ "
sin
"
#
#Ð#
#Ñ
#
#
# "
"
#
#Ð
# "Ñ
4.
Find the area of the surface obtained by rotating the curve
about
C œ
ß " Ÿ B Ÿ #
B
"
'
#B
$
the -axis.
B
1
1
1
1
1
Ð
#Ñ
Ð
#Ñ
Ð
$Ñ
"&
%$
"&
%(
"$
%
"'
#
"'
#
ln
ln
ln
5.
A gate in an irrigation canal is constructed in the form of a trapezoid 3 ft wide at the bottom,
5 ft wide at the top, and 2 ft high.
It is placed vertically in the canal so that the water just
covers the gate.
Find the hydrostatic force on one side of the gate.
(a)
(b)
(c)
(d)
(e)
lb
lb
lb
lb
lb
#
#&
#'
##
$
$
$
$
3
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) † '#Þ&
† '#Þ&
† '#Þ&
† '#Þ&

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