t2s2_20081108 - meme Ml(WWW/WE Est'wl Nodal SOLUTIONS...

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Unformatted text preview: meme; Ml (WWW/WE» Est'wl Nodal SOLUTIONS? University of Toronto at Scarborough Department of Computer and Mathematical Sciences Midterm Tee ——-— See @ MATABZ — Calculus for Management I Date: November 8, 2008 E. Moore Duration: 106 minutes Examiners: R. Grinuell P. Grover Signature: rIutorial Number (eg. TUT0032): Carefully circle the name of your Teaching Assistant: Talmage ADAMS Wenb'zn KONG Sean TRIM Eric CORLETT Carmen KU Alfred YlP Minn DANG Alex LUCAS ISan ZHANG Mikhail GUDEM Chris LUI Yichao ZHANG Molu SHE Xiaocong HAN Read these instructions: 1. This midterm test has 10 numbered pages. It is your responsibility to check at the beginning of the test that 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 and clearly indicate the location of your continuing work. oints will be awarded only for solutions that are correct, 3. For the Part B Questions, full p oncepts and methods of MATABZ. complete and sufficiently display {3 ulator. The following devices are forbidden: laptop 4. You may use one standard handmheld calc phones, l—Pods, MPeS players or similar devices. computers, Blackberry or similar devices, cell- 5. Extra paper, notes and textbooks are forbidden. 8 j SOMQ no‘l’ 0?9€&( - Qfii Mtdlemw Cox} (at wT'Hx Do not write in the boxes below. Part A - Multiple Choice For each of the following, carefully circle the letter next to the response you think is correct. Each right answer earns 4 points and no answer / wrong answers earn 0 points. Justification is not required, but a small workspace is provided for your rough work. .1. 1. The séope of the tangent line to the curve y = x 2 5 :1: at the point where a: = 2 is (a) 3/2 (b) ~1/4 (C) 2 2. If p :2 ~2q + 80 is a. demand equation Where 0 < q < 40, then we have unit eiasticity at (a) no vsiue of g (b) q m 24 (c) q :3 16 q 2x 20 (e) a vaiue of q not given by (a)I (b), (e) or (d) * 3 w/ g M .5 n Fab) "*2, “'2, :2. ‘ ._. {5.2 3. If y is defined implicitly as a function of 3: by fihe equation 232:2; —i— £n(y) —n 6% = _9 then the vaiue of y ’ at (3,1) equals @ 0 (c) —2 n i . (e) 2 (d) none of (a), (b) or (e). 4‘ For x > 0, let f(:z:) = ask Where k is a constant and 0 < I; < 1. We may conclude thet f ’(x) is decreasing on (0, oo) (o) flm) is decreasing on (0,00) (10) f ’(m) is increasing on (0,00) (d) none of (a), (b) or (c) is true 1| 3 VLF-2" Hf a: 0 fl: twist ab 1? w 40 >3 90 «13 (K) 55 J? 5 If u=(e:c)‘/‘E then g: _1 equals (a) e (if; (c) 1 ((1) none of (a), (b) or {c} 41—): ( i~+ IQMMB 6. If Mt) = 2(3t) then mm) equals (a) anew (b) o @wno)? (a) 21x49) t’m: fled/UM?) 800 7. If the average cost to produce q number of units is given by E m m then the marginai cost of production at 14 units is (a) #2 (b) 380 (c) 48 (d) 38 not given by (a), (b), (c) or (d) m 800 C: Cari: at, 0m e 8. Exactly how many of the following four mathematical statements are true: If (i) A rational function is discontinuous only at points Where its denominator is equal to 0. F (ii) A function g is differentiable at 3 if and only if g is both continuous and positive at s. F: (iii) The domain of a function H is the same at the domain of the function H ’ . F (iv) If f ’(a) m 0 or f’(a,) is undefined then f has a relative maximum or minimum at a. ({1} three (e) all four Part B w Full Solution Problem Solvirzg [8 points] rer finds that when 2, 500 calculators are produced per day, the average producw ‘2. A manufactu $8.35 Based on this data, approximate tion cost is $31.50 and the marginal production cost is to two (correctly rounded) decimals (a) the production cost of 2, 501 calculators per day E(;25w) ; ghee 3-: C(ZSW’) [5 points] . i _ Chem) “:2 C(2sw3 ~t— C (2.900) a: @[u 13:300.) 8:3 33”“1 + C“1 3. in ail of this question let f (:13) = where c > E) is a, constant. (a) Find the point(s) at which f is discontinuous. [3 points] «L. 4- 4— fima H So fi‘ié $XGCWF‘wwS X 6 ed” 0 (kiwi (L is no‘i’ dean‘iud 00% E“) GKV\O( {Evé is 0 Niven 7C5C> (13) Find the value(s) of c for which f ’(3) = 1/2 [? points] amt W??? 1f- OLS 10PM:— .__EZ’L» :S-i 3 WW C '- 7‘. CH‘F CNL' a ’m, ___._ 2C “ (64)?” new)?” i (F! 2c: M 1 c a (3) a: “‘fi“ " e :1 (0-3)” CZ“ QC+01 [21> Czar (at? 01 3 4 C c1.» {Dc + 0] :2 O (c -- “Xv—Pi) :«h 0 3‘ F;(+;2r~2' 4. A positive reek number T has the property that “its cube is one more than twice its square” whose leaéing coefficient is 1 such that r is a (a) State the cubic poiynomial function f (:3) [2 points] root of f . lino: X3!— sz“ wi (W W 4m 0) (b) Justify mathematicaély why a“ E (2, 3) [3 points] hence d3 gm [2&3 m 2 to find 272 and $3. [5 points] (e) State the Newton method iteration formula and use it with 231 Use four decimals in your answers‘ \(3 x 2.10?— 1 7 1/5 ,. 5. in all of this question let 9(3) : 335/3 + 5332/3 a: X X ~f— b (a) Verify that g’($) 2 52:33) [4 points] I ‘75 “1/3 (a (“m r: E ‘L .t E; 7; 3 *5 5(x+2 i. A (w- 23 1’ > ‘/ -3x@ critical values of g and determine the open intervals on which 9 is increasing (b) State the [6 points] 0? decreasing. Sufficiently justify your answer. $i("7/l '5" O 50 ’2 TS cat CWT‘FI‘COL/l it 9‘ rs umelefimci ml 0 Sci" 0% alas 0L wilted its.» \ we?» w 6? “t "F ’1' t W ____ W (D .—+ mg tbl‘s ladeokswg am (woO§HL>Ci-r<(9)c>0) €325 Alan/master? cm 6—” 23 o) C 0 V\ (Ll ll glorng (Wire, 91543“ W (Ll/\(XFSF calm we .9 > 8 Question 5 continued relative extreme of g and the corresoonding function values (5) to two decimals. Sufficiently gustify your solution. [5 points] (0} Find the rt-values of the there. Round your answer 5‘1" Bugs 713T; {NE 0K Vdm‘f'i‘vfl max @ “72a 0‘?’ Values j{»2,‘)=;(_.2) (:5) 9...,” ((1) Find the absolute extrema of g on the closed intervai [—1, 1/2] 1‘5- [5 points] 9; (33‘s Cmvhyttwt}; mfle deem“ loomed s‘ya/M “We CteSecq Mefiwfi “P6” CXJXEEEEIHCE Méi‘CWK GOiWéfi ‘-Hr\{ WW, 6. Find the equation of the line having negative slope that passes through the point (2, —«~3) and is tangent to the curve 3,; m 32 + m. :1 ‘ \ - r - X ( we \ ) [8 points] ...
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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.

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t2s2_20081108 - meme Ml(WWW/WE Est'wl Nodal SOLUTIONS...

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