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MAT136H1
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Anthony Lam
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# MAT136 2010 Term Test 1

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Western University

Mathematics

MAT136H1

Anthony Lam

Summer

Description

Code: 4576
DEPARTMENT OF MATHEMATICS
UniversitvofToronto
M.{T 135Y
Term Test f3
Wednesday, March 3,2010
Time allowed:t hour,,45minutes
PEN:
PLEASE PRINT iNINK OT BALL-POINT
NAMB OF STUDENT:
(PleasPRINT fullame
andUNDtrRLINE surname):
STUDtrNT NUMBER:
SIGNATURE OF STUDENT
(inINK orBALL-POINT PEN):
TUTORIAL CODE (..gM4A, R5D, etc.):
TUTORIAL TIME (..gT4, R6,F3,etc.):
NAME OF YOUR T.A.:
NOTE: FORMARKERSONLY
QUESTION MARK
1. Beforeou start,eckthat thisestas 14pages.
PAFUT A l48
ThereareNO blankpages.
B1 / (
2. Thistestastwo parts: B2 / n
PART A marks]:12multiplehoiceuestions. / t
[48 B3 ln
PART B [52marks]:7writtenuestions. / t
B4 l7
Answers to bothPART A and PART B areto begiven in
thisbooklet.No computer cardswill beused. B5 / x
3. No aidsllowed. B6 /R
No calculators! B7 /R
4. DO NOT TEAR OUT ANY PAGES. TOTAL I100
Page 1 of4 Code: 4576
PART A [lrSarks]
Pleaseread carefullv: your
PART A consistsof12 multiple-choiceuestionseach ofwhich has exactlyne correctanswer.Indicate
answer toeach questionby completely fillingn the appropriate circlewith a dark pencil.
MARKING SCHEME: 4 marks for a correctswer,0 fornoanswer or awrong answer. You arenot required
that forPART A, only your final answers (asindicated by
to justifyour answers in PART A. Note
the circles you darken) countl your computations and answers indicated elsewhere will NOT
count.
DO NOT TEAR OUT ANY PAGES.
- and : e* 10,then :
1. Iff'(r) e** 8r /(1) /(0)
@ B
@ e
@ 1 1
e 7
@ 1 0
- by partitioning into3 subintervalsf equal
2. Find the Riemmann Sum torf (r) 2r * L on [1,7], [1,7]
lengthand choosingeach sample point to be Lheight endpointofthe subinterval.
o 6 6
@ 5 4
@ 4 2
@ 7 2
@ 4 8
Page2 of 14 Code: 4576
It d,r 5 and - 5g(r))d,r 40,then [email protected])dr -
3. Io^@) ttQf @) In*
e -6
-L4
@
@ -12
_B
o
@ -10
- ( 2 t t - t - 2 ) ( 4 t + r -
4.If G(r) Jo L + t 3 dt,thenG'(27
16
@
@ L4
@ undefined
O I2
@ 10
areaf theregionoundedby thecurves r * 2 and - 12+2.
5. Find the U: A
1
@ 5
ov 3?
1
o ;
I
9 5
1
@ i
Page3of14 Code: 4576
6. Let Rbe the regionbounded bY thecurvesy- 1ftandA:12 Find the volume ofthesolidgenerated
byrevolvingR about theY-axis.
7T
@ 4
3rr
O ,
7T
e 5
7T
@ 5
3r
t v T
7. The averagevalueoff (r) I + 2r* 3r2 on [t,3]S
@ 2 4
@ 2 0
@ 3 0
O 1 8
@ 1 6
Page 4 of14 Code:4576
8 l,'1 . + r * 1 2 * 1 3
1
@ n(" +In2)
1
@
i("+ln2)
1 -ln2)
@

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