Dec 2004 Term #2 - $lv€j nun-M Department of Mathematics...

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Unformatted text preview: $lv€j nun-M Department of Mathematics I I I University of-Toronto I I TUESDAY, December 14, '2004'9:0’O—11:oo AM I" ' MAT 133Y TERM TEST #2 ~ Calculus and Linear Algebra for Commerce Duration: 2 hours 1. Aids Allowed: A non-graphing calculator, with empty memory, to be supplied by student. Instructions: Fill in the information on this page, and make sure your test booklet Contains 11 pages. In addition, you Should have a multiple-chdice answer 'Vsheet, on 'which you should fill in your name, number, tutorial time, tutorial room, and tutor’s name. This test consists Hot-10 multiple choice questions, and iiwritten—answer questiOns. For the multiple choice queStions you can do your rough work in the test booklet, but you must record your answer'bycircling the appropriate letter.» on the answer sheet with. your pencil. Each correct answer is worth 4 marks; a question left blank, or an inCorrect answer, or two answers for the same. question is worth 0. For the written—answer questions, present your solutions in the spaceproyided. The value of each written—answer question is indicated beside it. ENCLOSE YOUR FINAL ANSWER IN A. BOX AND WRITE IT IN INK. TOTAL MARKS: 100' ;- . . or.szan : u STUDENT NO: SIGNATURE: TUTORIAL TIME and IROO'M: REGCODE and TIM_ECQDE: . TATE NAME: Regcode T0101A MQA P11010113 M913 ‘ _ T0501'D T0101o __ I ' rosom T0201A I ' T0701A T020113 T070113 T0201C TOYOIG T0201D . TosmA TGSOlA ' I MP .137 "11080113 FOR MARKER ONLY Multiple Choice - B1_. 11030113 UC 32s T5101A 1103010 MP'134‘ 'T510113 T0401A 1311‘ 323 T5201A T0401B LM 123 T0501A LM 123 _ T0501B UC 328 Page 1 of 11 I NAME; _ I = - ; e ; - 7 ‘STUDE.NTZNQ:I_._ ' PART A. Mnltiple Choice: 1. marks] ‘ ‘ ‘ V. I fl; _. The derivative of fix) 2 ' . Hem+2i _ '- @X%l)(lx)fl (Nerdy W . (ex-+1)? 2. [4 marks] . Suppose we know that the function f doee not have-a. maximum value on the interval 0 S w E 3 .‘ Thenlwe can be sure that: :_ - fl? 7' 96:) g :1 (Q0 Wang); A. f($) : l Causg be: many 42% (“it "5’7 ' mt} tiger “"53 ‘ :1: f($) is not continnqus on [0,3] C. The deriyative of f($) at 9:: 1 does not exist Hugged? firm“ a t“ _D.. The interval 0 g a: g 3 ie' not Closed 1% '3: do; 5&- E. f gets bigger than. any given number on this interval. I . No. bad-[0.3g- $93 . ’_ i.x agxaf‘g _ - ea) ’— . - . - 0 - X" a 3 chfi {0’3} U I 6.2m .fimg ' have a m wfi‘ifl‘) Page 2 of 11 NAME: 3. [4 marks]- lim ‘00 1 +6” equals —3 . equals #1 C. equals 4 D. equal-s ,_ E. does not eXist ' 4. [4 marks] equals 1 '- x/g __= equals ——. C. equals 3 D. equals 0 E. does not exist 4—38”‘”_- STUDENT N0: Page 3 of 11 I NAME: STUDENT NO: _' 5. [4 mqus] _ The annual rate?" compouhdgd QQntinuously‘which is equivalent to 6% compounded quar— terly‘is closésfi’to: ' ' 'v- r, f é} . A. 5.83% - Q "-7- Q+L%') ‘ B.‘ 6.05% ‘ I I 7 I ‘ 4 1.0!? 5.96% r ’ ' D. 5.9% - _ I ‘- I z E. 6.14% f}; 05%”? 6. [4:ma'rks]. ' The solution of the inequality 2 0- is given. by: -(Q;—;<I1+2<)- 4—232 A. ~4<$<—20r1<m<2_ B.$§_#40r—2-<$§10rx>2 C. 413323—20: 13i$§2 D. LBS—.4 or —2§-m§1'0rm22 ~4g$<—2 or 1gm<2 Page 4 of 11 NAME: 7 ' STUDENT NO: 7. [4 marks] Given'that f(0) = 2 and the siope of the tangent” line to the graph pf fix) at the point (0, 2) equals 3', the slope of‘the tangent line to the graph of at :17 2 0 equals A: 80 . ‘ ‘ Y‘zgyfic11f I I I ' _ Ya, {magma 3’5 We): 5EWT’W} 8. [4 marks] If y : y(:r:) satisfies 'y”: _= 61‘", then when (my) 2 (2J5, J5)? — : Page 5 of 11' NAME: _ I I STUDENT NO: _ 9.' [4 marks] If $1 751 is used as an initial estimate for a‘solution of flit) = 0, when : than NeWton’s method yields the sedond estimate :32 z , A. :61 - I I a ,... WI. 2 _.Q(x):_my 13.0 1+0. [4 marks] - 1. . - 1 If y($) = 1) (—3: + 1)2 + 1)3 (Zmr+‘1)4 + 1)5, then y’-(0) : E _ l - L.“ i , + ,_...L—-—-—-v+ W k5; . 437?" “$273”? 2:5” are w «M Page 6 of 11 NAME: ' _ ' ' - ' STUDENT NO: ' PART B. Written-Answer Questions 1. [14 marks] Given 1 5E M < 0' 2 — 2:1: ': ' 'f 0 < < 2 flit?) $fi2 1 _33 4b . . w— 1f :2 2 2, Where 1) IS a constant. Showing your steps clearly I [’7] ((1) determine Whether is continuous at a: r 0. 956:). __ 5”?" _' on Q”) "as! _ Q (I) gig-‘2‘”? Y4E+ ‘I _l_ h ; 61? a); (-Yé OVA ?‘ A) w a ‘K . .41 . jg} I I I . j?€1)“';ufl' égé ‘gk> “Afiw 5' “ ' xsl ,umuwww a A Page 7 0f 11 NAME: _ - . STUDENT N0;- 2. [12 marks] .Unit price p and demand quantity q for a certain good are related by the equation Where p is in the range $500 S p 3 $700. d Find the marginal revenue Egg where p is $600. Page 8 of 11 NAME: - " - ' . STUDENT NO:_ 3. [16 marks] If a demand curve is given by _ q2 .+ 'pr + 2102 z 1100 [8] (a) What is the (point) elasticity of demand when (1 : 10, p = 20 ? [8] (b) At the same point, q z 10 , p : 201 is the demand function Mg) concave up or concave down? Justify your answer. [This is not an invitation for an'essay on demand curves; the question is about this demand curve only] I aid 4 (EL- We Comtfli/ Mile, £14m“? Ifaa’fiv If?) t/th’é‘ ( a a w H) ‘ 1 E3 Seéfigfé‘t Wt 9&3; W am W m'iwté‘fli 3’ w .2, gm t2? flfflgfiai NAME: ' - ‘ '~ . STUDENT N0:-_ 4. [18 marks] Given ' 2 1 an that I- 18,313) I ) '7 and fHW) : .then, on the way to sketching the graph of y : f , justifying your answers, (a) find all vertical and horizontal aysmptotes if any ' (b) (c) find where f is concave up, concave down and all inflection points if any i (C1 New sketch y z , shOWing all the features in_(a), (b) and‘gc). 06) find Where f is increasing, decreasing and all relative extrema if any Question 4 continues 011 Page 11 Page 10 of 11 NAME: ‘ - ' STUDENT NO: (BLA SHEET FOR QUESTION 4) Page 11 of 11 ...
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This note was uploaded on 03/02/2010 for the course MAT Mat133 taught by Professor Igfeild during the Spring '10 term at University of Toronto- Toronto.

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Dec 2004 Term #2 - $lv€j nun-M Department of Mathematics...

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