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Unformatted text preview: SIMON FRASER UNIVERSITY
DEPARTMENT OF MATHEMATICS Midterm 2 (v.1) glut .77)
MATH 152 Fall 2009 Instructor: Dr. L. Goddyn (D100), K. Doerksen (D200)
November 4, 2009, 8:30  9:20 am. '/
Name: /K' e (please print) family name given name SFU ID: student number I 5FU~email Signature: Instructi0ns: . Do not open this booklet until told to do so. . Write your name above in block letters. Write your
SFU student number and email ID on the line pro
vided for it. Put your signature on the line provided. . Write your answer in the space provided below the
question . If additional space is needed then use the
back of the previous page. Your final answer should
be simplified as far as is reasonable. . To receive full credit for a particular question your
answer must be complete and well presented. . This exam has 5 questions on 6 pages (not includ« 
ing this cover page). Once the exam begins please Tota; 
check to make sure your exam is complete. . No calculators, books, papers, or electronic devices shall be within the reach of a student during the
examination. . During the examination, communicating with,
Or deliberately exposing written papers to the
View of. other examinees is forbidden. MATH 152 Page I of 6 1. Compute the following integrals. You are encouraged to specify the integration technique
used for each integral. [4] (a) / tan298ec49d9 l _ L Silésf/i/[u/e LL; {an d“ : 556 1? (1'70 13 (2L1 (MEH) dam 3 _
' {gusrf'gu .tc ,, \i ‘ 3 3 a
7% We 5’ t {can (3/ .,L C MATH152 Page 2 of 6 2. Compute the following integrais.You are encouraged to specify the integration technique
used for each integral. [4] (a) fmdt 556 (V 7) :c+2 [4] (b) fwdx [any (IEV’iJl‘EK
1.1 +3 I _ “DC+1) 7.11 + 7/11 + 7 3 L1. +3 ‘i’ DUDE {/J‘ 2%?“ + qJL
_M
3% 4'?
3.9L 4’ 5 A4 [Vii “t C "L
«3 DC +3Xt : MATH 152 Page 3 of 6 2 1 566 (V11) MATH 152 Page 4 of 6 3. True or False. lf True provide an explanation, if False give justification (for instance
give an example for which the statement doesn't hold). [2] (a) (Ex—4 A B can be put in the form — + for some real numbers A and B. [332+1) a: $2+1 .526 Z) DO
[2] (b) The improper integral / 8—1 d1 converges.
O . Set; (ll/:1)  [2] (c) If P(:E)/Q(a:) is a rational function with deg(P) < deg(Q) and Q(:z:) factors as a
product of distinct linear factors (2 — 0.2) then f P(:z:) 62(33) d1: is the sum of loga
rithmic terms Ai in(x — ail) for some constants A: plus a constant of integration). See (v.1) [2] (d) If [:0 f(:c) dr and famgkc) dz are both divergent. then fax + dz is
divergent. gee (“1) MATH 152 Page 5 of 6 1
[5] 4. (3) Use f(x) = as 6 [1,5], and Simpson's Rule with n = 4 to approximate the area under the graph of y = ﬂat) for 1 S :c S 5.
Note: Put your answer in the form of an improper fraction. / [3] (b) Let Sn and .310“ be two Simpson's rule approximations of f(:c) due, by using n
and 10p, intervals respectively. Suppose Sﬂ can be trusted to 5 decimal places. How
many decimal places of 510” can you trust? 52:96 (V 1) fl'fATH 152 Page 6 of 6 5. Compute the following integrals. [4] (a) fosmildli l’lffJ Val'lllfrf/ eijmfﬁr/c.’
t M 1:1
‘. L dz 3 )L
t—vr lr P x t“); t
W? “ff” ﬁlg mll l}
, Ill¢1 In Ier’:] : /;mq In lt_d __ L4 I,“ f“? I 'v’ for
_ 12°00
Sc? lmlt’ym/ .5 lv’c’t/y‘c’)’ [5] (b) [To 226* d1 556 (1/. 1) SIMON FRASER UNIVERSITY
DEPARTMENT OF MATHEMATICS Midterm 2 (v.4) aux (If. 1)
MATH 152 Fall 2009 ‘ Instructor: Dr. L. Goddyn (D100), K. Doerksen (D200)
November 4, 2009. 8:30 — 9:20 am.  Name: (please print)
family name ‘ given name SFU ID: student number ' SFU—email Signature: Instructions: . Do not open this booklet until told to do so. . Write your name above in block letters. Write your Maximum
SFU student number and email ID on the line pro
vided for it. Put your signature on the line provided. 
. Write your answer in the space provided below the  
question . If additional space is needed then use the
back of the previous page. Your final answer should  
be simplified as far as is reasonable.
. To receive full credit for a particular question your  
answer must be complete and well presented.  
. This exam has 5 questions on 6 pages (not includ 
ing this cover page). Once the exam begins please 
check to make Sure your exam is complete.
. No calculators, books, papers, or electronic devices ' shall be within the reach of a student during the
examination. . During the examination, communicating with,
or deliberately exposing written papers to the
View of. other examinees is forbidden. MATH 152 Page 1 of6 1. Compute the following integrals. You are encouraged to specify the integration technique
used for each integral. {4] (a) /tan36’sect9d6 : ié‘eclﬁli 565:: (23 661:. cf? vii/5) @135 tinifﬂ i
I (A: 55C 7 7’ if; 1 5‘?  6.3 5,? (My
:[(9541)(7{£[ C L ‘LC )‘
M : ——— —M, ‘i' C
i 3 3
arse: e “5666:? + c
. 7 r' ‘f'
[4] I fetSintdt 1.7: [Dds‘I/s UL; flit: L: {I {7 r 1 [Afa— Lm {‘ {f ‘1 git
T: e i  jg t w— _
H ' A . r t
By Width ﬁfjjcifﬁ V566
(AF: ~14}: L" 3: MATH 152 Page 2 of 6 2. Compute the following integrals.You are encouraged to specify the integration technique
used for each integral. 1 _
[4] (a) /t2+2t+2 dt Camﬂ/Wzﬁ 'HW .Sf/v'ilfﬁ‘i
. '1 I, “571406 b‘v/QC : ('0
(W H [4] (b)/t2+t—4dt  . l \
t+3 QIL/Af/C/Vk ..(:_7‘ . 128) z. g ml. m l; "‘t ‘/
2ftng '5” 0“ (“Mt : {1:215 +1 /m [6+3] + C ‘15 ‘é MA TH I52 [4] x; 1 .M . ,
v2\/,U2—_f dv .5“ Page 3 of 6 U: 56: V,“ 3 £7?“ (7‘ Why“ (f: 122:1 0:17;»
/ ‘1
V’Z'! "g 1 if ._ 'Tf'
I L if V— 2_ 1 Cf, 5)C?‘1I’3/1‘V1%§/K=at/ If
[ {73:4 . {C712 9 0(6)
_W
L A‘ .
"Tr 55° 9 ,/_
‘i
“6’
.,_ {7291 ,
’ A d 6(6)” 63
"2 I,
“2 W: : . m 3 551 cf?
1 f5“ Q (15;
3
.— l _" “I ﬁ
,. 5H1 A! 7’2! g ‘n’ S {1’
.3; 5H4 *’ Jun 4' 2. M;
"V;
w .5 l A L’ 3 _ [/ZI I
5" V 73 2x MATH 152 Page 4 of 6 3. True or False. If True provide an explanation, if False give justification (for instance give an example for which the statement doesn't hold). (a) x m can be put in the form £ + B (332"; '1'“) a: 332 +1 for some real numbers A and B. . ‘L ..._V I , d . I f» /l ha /5 € {763651 “5/? f»  B :— f” i "LB L m
.r' ‘“ X. 9th» I )L (A f“ I) {flit .575 ff “.1 C7 . . B  I he; we 16!»; firm: _____..._—..._.._.., 53 MM [2] [2] 00
(b) The improper integral / 6—1 alas converges.
o ii
P’— .\ f w r l l‘me, .51“? lim { e 10%, "1: Am ~61]
few 0 {gawk}  {a
\ "LL ~. . "E
2 l2: we :i (c) If P(a:)/Q(:z:) is a rational function with deng) < deg(Q) and Q(.t) factors as a
product of distinct linear factors (a:  at) then f P(x)/Q(x) rim is the sum of loga
rithmic terms A; ln(2: w ail) for some constants A. (plus a constant of integration). [Pl/if Sld’tf'g . (we) .___.___—4
f0 a; jam (PK fawn/(5 If); e'L/ﬂCZr/JJ fig/“Ail / 15V a 57/; (fl/1 5‘ :" Wt X,  (L ; (d) if fawfﬁc) dm and faoo 9(22) dz are both divergent, then' fam + dz: i5
divergent. J 70er excxwp / ({mﬂK S _[
fhém I jawed
9° ‘9 0‘, .6.» I/‘(ewéqm 7:. gm = M (00) a 0. m. ‘j d‘ a
2% gram (P MATH 152 Page 5 of 6 1
[5] 4. (3) Use f(x) = :1; E [1, 5]. and Simpson’s Rule with n = 4 to approximate meek under the graph of y = f(:i:) for 1 g at S 5. i I 3 v.“ 3 “my Note: Put your answer in the form of an improper fraction. ./’l:'/’\6(,‘t 4“!“ S1 A“?
_ f L “
3 (PM * “i lear 1 lea) t WM) t lml
,/
‘L l
:Jv(L“t it ﬁll—(1+?)
3 l 1/ 3 i1 5
, w, _  L “L3: r t LE: 1‘ w:
3 )4, I5 Is ls l)
I ' — ’g ( 15’s,,
e 73
‘if
[3] (b) Let Sn and sum be two Simpson’s rule approximations of ffﬂx) dx. by using n and 1071 intervals respectively. Suppose Sn can be trusted to 5 decimal places. How
many decimal places of 5'10” can you trust? Wt}, aft/e 1/923?” ‘H/ixll fin/Wm" 0/: if all waif 5 " 5* was”
Klilsm 5” O M
The (2 VV (1' V" g} F j [genre {Ll/e a era’f—
_ . 5, mm . ‘ 5’
K [ . ~ 6%) : {mewL) f “2— Li
I Q (It? m)Ll mil  ' _ w"i’
4 f0 5“ f0 7 “~—‘ M“, H immemmwayhmﬂmamm MATH 152 Page 6 of 6 5. Compute the following integrals. [4] (a) [fring ’ 3
t dim 1: l/WL lit1 f" I'll/1+ “"1
tag“ ° tﬁl C ?
t
; I’M Im [1,1]] + [IMF ln [Aral]
tﬂl' . "0 {ﬁg t
g:— w w w e l w ElyH; mil: 57/49 .221 it; ‘lL (L:  50 EA E [314 ‘llf'ya/rg/ dflV/thyr’ (’5. ' [5] (b) [0 me‘mdm f, ‘1
.5; 4' 13“ LLLPL U'irff l ‘9( «BL. *1 f_ ‘ a.
J3me d)» : ',>ce] [*6 a!» ctr! U=~€l
0 U ‘3  . ')C :c f
: “ace + (C . t 13 *0
' “f E’ —e  (0— e )
u. «t ~15
~ {*t8 6
50.70 f
A. __ at g
I
.15 (It 1 AM fig (ZR  ﬁlm”! I— ‘C
tﬁm [950
0 v ...
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 Fall '08
 GREY
 Calculus

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