Midterm_20071029 - SOLU T70N€ University of Toronto at...

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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 name-of 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, cell-phones, I—Pods, NIP-3 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- \(i - l 3. Assume your annual salary increases from $ 40, 000 to $ 60, 000 over a four year period anti that each annual increase occurs at the end of each of the four years. The annual rate of your salary increase is approximately 10.67 % (b) 5 % (s) 12.5 % ((1) none of (a), (b) or '/ (-00 :4OCI1- rfl :5 {7,414 ’V r 3066 4. If Mt) = W -- %1n(5+2t) then the value of L31193505) is (a) o ' (b) —1 @—§ _ (d) amassed Note +kw‘r (“29+ 5(—L)7‘«%2(~2) _ 3 a “2 4M” H L—z)‘+ (~23 ~2. 0 0 +( J . c’; .2. *\ - «(+3: PM _ —r é— Maze) (176%ch l c.2301) :. film 5. If f(2)=2, ff(2jm3, g(2)=2 and g’(2):—5 then (a)(9~f)’(2)m-2 (‘0) (2) -1 (C) (f9)'(2)=-15 (90f)’(2)=_~l5 74 ‘74 X 1| ‘___‘_ 3 (2).}: (2.) :5 515); -—~ :5 6. If the average cost to produce q units is given by E i @9— then the marginal cost at a _ q + 5 production level of 5 units is (a) 60 30 - (c) —6 (d) 300 T. To three decimals, what approximate annual rate of mterest compounding continuously is equivalent to 5.6 % APR compounding quarterly? (a) 5.483 % ' (b) 5.644% @5561 % (d) none of (a), (b) or (c). r 7 . .055 4 .05; 6 3 l + __ .— ( 4- ' - N v 0 5 5&2 l 8. The $~i11tercept of the tangent line to the curve 39 = 2:13 ~§« “ii at the point Where m 1 is (a) nonexistent because the tangent line is horizontal mg (C) 1 —1 .4 ,5 03:27C4-X 2‘ 43’:Q—;LX l2" \fimz’é . (3,0)“ *3: g: :‘Tavxaewl’j/Me €01: l5 (3-- =§(’K~‘) Part B - Full Solution Problem Solving 1. (3.) Find fihe exact vaiue of f’ (2) Where f($) = (2n: + 1)(6 u 5:17)(27 + 9) —§— 2‘" [6 points] f”...— 41;“? 2(é-SK)(XT‘O\) *t @I$+\)(~5X¥tq) + (wax-(a ~51<)(\) + 2U;ka yup (MK-MUN) + LS)(-s)(\\) draw-AX!) + 25am.) 3 .— 335 +1MW} . war/*WM~ flo den/1M5 ). (b) Calculate the exact cc-coordinate 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 kofiéoww-I 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 nearest-dollar). [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.242-5 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(gL-q 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 PreH-QM !, )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 C-er'tu‘uxLa COK‘HALLDUS on (“‘00) “ cahl. gr CootfinuH-j 0:" 3‘ we need 42W 61 { Jiwfiffl;#/g) (£(g); 3c+\) fl x—-‘>5 (EMF-WC”); 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 serrfi-annually 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 . (gawk-A? 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‘V-e 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 Mam-es) hm 8+ 4“ % ft 3 "WHO 4(1+h)%5+3 $5 McN-iPX/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.

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Midterm_20071029 - SOLU T70N€ University of Toronto at...

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