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Unformatted text preview: SOLU T70N€ University of Toronto at Scarborough
Department of Computer and Mathematical Sciences Midterm Test MATA32  Calculus for Management I Examiners: R. Grinnell E. Moore ' Date: October 29, 2007
X. Jiang T. Pham Duration: 110 minutes Clearly indicate the following information: FamilyName: O U C) M S Given .Name(s): Student Number: Signature: Tutorial Number (eg. TUT0032): Carefully circle the nameof your Teaching Assistant: Marc CASSAGNOL Carmen KU Alexander WONG
Paula EHLERS Jack LIN Calvin WONG
Xiaocong HAN Chris LIU  Yichao ZHANG
"Mohammad KOBROSLI Amreen MOLEDINA Xiangqun ZOU
Wenbin KONG Molu SHI Read these instructions:
1. This midterm test has 11 numbered pages. It is your responsibility to ensure that, at the
beginning of the test, all of these pages are included. 2. Answer all questions in the work space provided. If you need extra space, use the back of a '
page or the last page. Indicate clearly the location of your continuing work. 3. With the exception of the Multiple Choice questions, full points are awarded only for solutions
that are correct, complete and sufﬁciently display concepts and methods of MATA32. 4. You may use one standard hand—held calculator. The following devices are forbidden: laptop
computers, Blackberry or similar devices, cellphones, I—Pods, NIP3 players or similar devices. ‘ 5. Extra paper, notes and textbooks are forbidden. l '50 1/ U :: :1_.   . a. .,.. .,.. .g . ._..l..._‘._, ‘11.”,
IA . ,;,_,53..: a: Do not write in the boxes below. The following formulas may be helpfﬁl: Sr— P(l+r)“ SmR[(1+:)”—1] Part A — Multiple Choice For each of the following, circle the letter next to theanswer
you think is most correct. Each correct answer earns 3.5 points and no answer/incorrect answers
earn 0 points. Justiﬁcation is neither required nor rewarded, but a small workspace is provided for
your calculations. 1. The present value of $ 5,000 due in four years at 6.6 % APR compounding monthly is about (a) $ 4, 891.50 (b) $ 3, 782.05 (C) $ 3, 935.49 _ $ 3, 842.65
"" 48 N 2. If ﬁe) = 1n (62$ + x) then the value of f’(0) is (a) undeﬁned  3 (e) 2  (6.) none of (a), (b), or l ; €21 l I 11'
“PM”: 27: 33> «F (0):: —~———: 3
e «t \(i  l 3. Assume your annual salary increases from $ 40, 000 to $ 60, 000 over a four year period anti
that each annual increase occurs at the end of each of the four years. The annual rate of your
salary increase is approximately 10.67 % (b) 5 % (s) 12.5 % ((1) none of (a), (b) or '/
(00 :4OCI1 rfl :5 {7,414 ’V r 3066
4. If Mt) = W  %1n(5+2t) then the value of L31193505) is
(a) o ' (b) —1 @—§ _ (d) amassed
Note +kw‘r (“29+ 5(—L)7‘«%2(~2) _ 3 a “2 4M” H
L—z)‘+ (~23 ~2. 0 0
+( J . c’; .2. *\ 
«(+3: PM _ —r é— Maze)
(176%ch l c.2301) :. ﬁlm 5. If f(2)=2, ff(2jm3, g(2)=2 and g’(2):—5 then (a)(9~f)’(2)m2 (‘0) (2) 1 (C) (f9)'(2)=15 (90f)’(2)=_~l5 74 ‘74 X 1 ‘___‘_ 3 (2).}: (2.) :5 515); —~ :5 6. If the average cost to produce q units is given by E i @9— then the marginal cost at a _ q + 5
production level of 5 units is (a) 60 30  (c) —6 (d) 300 T. To three decimals, what approximate annual rate of mterest compounding continuously is
equivalent to 5.6 % APR compounding quarterly? (a) 5.483 % ' (b) 5.644% @5561 % (d) none of (a), (b) or (c).
r 7 .
.055 4 .05;
6 3 l + __ .— ( 4
'  N v 0 5 5&2 l
8. The $~i11tercept of the tangent line to the curve 39 = 2:13 ~§« “ii at the point Where m 1 is (a) nonexistent because the tangent line is horizontal mg (C) 1 —1 .4 ,5
03:27C4X 2‘ 43’:Q—;LX l2" \ﬁmz’é . (3,0)“ *3: g:
:‘Tavxaewl’j/Me €01: l5 (3 =§(’K~‘) Part B  Full Solution Problem Solving 1. (3.) Find ﬁhe exact vaiue of f’ (2) Where f($) = (2n: + 1)(6 u 5:17)(27 + 9) —§— 2‘" [6 points] f”...— 41;“? 2(éSK)(XT‘O\) *t @I$+\)(~5X¥tq)
+ (wax(a ~51<)(\) + 2U;ka yup (MKMUN) + LS)(s)(\\)
drawAX!) + 25am.) 3 .— 335 +1MW} . war/*WM~ ﬂo den/1M5 ). (b) Calculate the exact cccoordinate of the p0int(s) on the curve y = (3:2 + 3338—256 where
the tangent line is horizontal. ' [7 points] ~27¢ “3/: (&*+3)6 “r Gﬁawbzﬂ
ﬁsh/6 3'30 Can/Lot Or; eaZ$K7~¥ +33% (¥2’+?>><)[~L)j ; €HL$[~ZXL “47‘ '55] 27c : .__. Z 15"(ML +ke 9460424 1—— Coercit‘MCFA A  5 NW4, ﬁxe— W+ , B koﬁéowwI M 2. A total debt of $ 7,000 due 3 years from now and $ 3, 000 due 70 months from now is to be
repaid by three payments. The ﬁrst payment is $ 4,000 at the end of 9 months from new.
The second payment is made at the end of 2 years from now and the third payment (which
is 65 % of the second) is made at the end of 50 months from new. If interest is 6 % APR
compounding monthly, how much are the second and third payments? (Round your ﬁnal answers 119 to the nearestdollar). [8 points] [WI “"795 “005 _...7 EM I: '7 . I 3
WC?“ { 03 t 9L  ® : . } 4m” l ' s ._ _ _ f
E‘lw‘d" W‘ 0'? Van”; Cambrde 4—0 70 New%% \ . (pl 7 4e 7 2.0 40000005) + $0.005) + éésxrlmos) 54
_:= 3000 + #000 (LOGS) 1.9?(oetx =~ S)%3"l.2425 l to! X: 2H?!" '5
’(951‘3 bqlglo ’17” 3. When 320 calculators are made during one work shift, the average cost is 29.55 and the marginal cost is 27.33 (both in units of dollars per calculator). Estimate to the nearest cent
the total cost to make 321 calculators during one work shift. [5 points] C :2 cost) ‘1’; Maxim mkothwsmp: C(51ﬂ C(3lb3 C [(32.23) “I: C(gLq MI (xii/(315) .E (132.0)
_—,—, .113 3 +@°l~ 551/310) l‘lfrsa. as} H 4. Find the Emit or, if it does not exist, brieﬂy state Why it does not exist. Use the or —00
symbols where appropriate. [4, 4, 4 points] . 5m~4$3+2 x+1
(a) wEI—nm( m3+8x2 + ) D COUfSL ‘ﬂwr‘j/l'emh’f'“ 1—x
413 7t heme; z
(b) 113% (exml ) (“walk PreHQM !, )Iy 'FHL); 81x L
z ’j'. 411M) 6‘00 a” 33’ (0) $21}; ((1 M “3)2 (a: + 3F) 1 90o omel Cl~¥)L«été M% (143)”
I: . ﬁ‘ MP} GLYNN/6 :5 "‘1 5O ) 50 EM E 5. For what value(s} of the constant c is the function f continuous on (—oo,oo) Where cm+l if 51:53
f(m)m{cxzm1if 33>3 Justify your solution completely. _ {8 points] \ 1
We QMthﬂ €914“th Jrov tuft, X73) wot iv}. for ¥€3,, LCM; 0“ ’H (?0\jmomm))so C43.
For X75; 9(1): C¥2~\ ( Poltgmmm‘) 56‘ 9+3 
A ' v e? T57 Cer'tu‘uxLa COK‘HALLDUS on (“‘00) “ cahl.
gr CootﬁnuHj 0:" 3‘ we need 42W 61 {
Jiwﬁfﬂ;#/g) (£(g); 3c+\) ﬂ x—‘>5
(EMFWC”); 1min“): 3C.“ We V\€v€0€
Way.) \‘(45 5C+{;O\C'—J
X‘M gnu :— Xﬁw’x (C¥2'*\) : D\C—\ SO C: 143+ “9“?”5"r 3 6. Suppose you win a large amount of money in a lottery. There are two banks in which to
deposit your good fortune. Bank A pays 5.4 % APR compounding serrﬁannually and Bank
B pays 5% % APB, compounding daily (1 year m 365 days). Which bank is the better choice
to invest your Winnings and why? [6 points] Wf, Compare VShM’j €4¥ecH¥€ roc’Fé§~
1 . (gawkA? re :0 29:36) \ N ' 0947’2‘1
05$ 365 I
Bath? {C:{i+ '"‘ N #094??? 3' We Bowed“ YWeslrtwA W:‘H‘ R
(XS H“ \AOLS 'er WSW Q'HRH‘Ve rouLﬂ. 8 ‘l
L
7. In all of this question let ﬁx) = m 2:, \ﬂ 2 + (a) Use the usual techniques of differentiation to ﬁnd f’(l).  [5 points] , ,7
pm: 3‘; (411+ 53 2' 03*) ., /_____§'_W__, 3
waif” 2(3) (b) Use the deﬁnition of derivative (ie. ﬁrst principles) to find 1“ _ [7 points]
WW ﬁrm; 3
Wm?“ @“M'ﬂ‘ﬂ
_ —’>0 k 5 \m ﬁAOMz—FS *3] W
N40 k
_ [m 4(‘+k)2+5 W 0‘ “w Mame»;
hm 4(+?¥\*4\«L+g*% WM Mames) hm 8+ 4“ % ft
3 "WHO 4(1+h)%5+3 $5 McNiPX/M +vP‘i’bﬁ’Ht—5w
L W W +3 8. Suppose $ R is deposited into an ordinary annuity at the end of each month and that interest
is 8.4 % APR compounding monthly. Let N represent the smallest Whole number of years
that it wilE take for the future mine of the annuity to reach an amount of $ 500R.
Find the value of N. ' [6 points] i rr HM J?I%bz \Amrs 10 (This page is intentionaliy 19ft blank and must not be removed) ‘11 ...
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This note was uploaded on 06/11/2011 for the course MATHEMATIC a32 taught by Professor Grinnell during the Spring '11 term at University of Toronto Toronto.
 Spring '11
 Grinnell

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