Spring 08 - MAC 2311 FINAL EXAM A SPRING 2008 A Sign your...

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Unformatted text preview: MAC 2311 FINAL EXAM A SPRING 2008 A. Sign your scantronvsheet in the white area on the back in ink. ‘ B. Write and) encode in the spaces indicated: 1) Name (last name, first initial, middle initial) 2) UF ID number 3) Discussion Section Number C. Under “special codes”, encode the teSt ID number 5, 1. D. At the tOp right of your answer sheet, for “Test Form Code”, encode A. o B C A D E . E. This test consists of twenty—two five point multiple choice questions, and 4 one five-point bonus question. The time allowed is 2 hours. F. When you are finished: 1) Before turning in your test, check for transcribing errors. Any mistakes you leave in are there to stay. 2) You must turn in your scantron to your discuSsion leader. ,Be pre- pared to show your picture ID with a legible signature. 3) Answers will be posted after the test on the MAC 2311 homepage. Problems 1 - 23 are worth 5 points each. m+9-—3 a: 1. Evaluate 11mm.” C) Doll“ H ODD-l a. b. c. d. e. does not exist 2. If f(a:) = gig—Ifg—‘E, find p and q Where p :2 limm93— f(:1:) and q =- ‘lima,__,_oo f(a§-). ~ a. 102—00 q=——2 b. p: —1 zq=2 c. pré+oo q=—oe d. p'="——00 '-q=2' e. p=+oo q=~2 3. Let (U snfw in < o 1:211:11 ifw>.7r/2 10(53): 8‘1 if0<cc<7r/2 Let p =1imm_+,,/2+ f(a:) q = limm_,0+f(m) a. p=+oo q=1 ' -b. p=+oo q=2 c. p = ~00 q 2: 1 d. p 2 —-oo . q = 2‘ e.pé+oe =0 ‘ Him we “Ti““ié 4. Find the value of K which Will make '_ «aw—k4 ifle 9(m)'.{m2+Kw ifa:<1 continuous at a: :- 1. a.K=e+31 b K=e+2 c. K=9-‘:—4 d.K=2-—;é e. K=4 5. Find limw.,4 fi. 3.0 ' 4_ b.92- 8 e Q 3' d. 268 e. 264 6. Fmd f’(m)-Where f(a:) = 21:1. 5; 3$~2 ’ (av-1)? b. Jig. (w—1)§ C. "i? (and)? d. _.2::_a;3_ (w—1)§ 4 z—l e._m_1 7. An object travels s(t) feet .in t seconds, Where 5(t) 2: t2 + 2(t + 1) 5%. Find the aCceleration of the object after t = 3 seconds. ‘ a. % ft/sec2 ' b. % ft/sec2 c. 12 ft/Sec2 d. git/sec? _ e. gft/sec2 - 8. Find f’(m) if f (m) = sin(ta,n2 at). a. f’ (at) = cos(tan2 :1:)sec2 :1: -b. J“ (:13) = 2 sin(tan w) cos(sec2 w) c. , f’ (:13) =, 2 sin(tan m) cos(tanm) sec 2 2m d.‘ f’(a:) e: cos(tan2 m)2 tan a: sec :1: e. f’(':::) = 2 sinactanmsec2 a: + tan2 :1: cosrc 9. Find the slope Of the tangent line to 51:23; 7—- 23: = 4\/§ —- 1 at («1, 1). a. 6 ' . 10. Find the maximum and minimum values of f(ac) = m on [—1, 3]. a. O, ——1 b. 2, —-1 c. 2, 0 d. 2, 1 e. 1, 0 11. The graph of f(:1:) =.m265"w2 has the following relative extrema: a. rel max: 0 rel min: :l:\/§ 13. tel max: film/5 rel min: 0 c. relmax: :l:1 rel min: 0 d. rel max: 0 rel min: .:l:1 e. f (3:) has no relative extrema 12. Consider the function f (:13) = 3:1: + 355— —— 25. The graph of f (:11) is decreasing and concave down on which of the following intervals? a. (—5,0) only I 4 b. (—o¢,—5) uf(0, 5) 0. (0,5) only d. (—oo, -—5) U (5,00) -‘ e. (—5,5) only 13. A rancher wants to enclose two rectangular areas near a river, one for sheep and the other for cattle. No fence is needed along the river. If she has 480 yards of fencing available, what values of a: and y will yield the largest total area he can enclose? - v a. :c =_120 yds and y = 60 yds flfue/ g b. 33:40 yds andy==180yds ‘ II‘ c”. a: = 80 yds and y}: 120 yds f d; a: = 120 yds and y = 120 yds e. a: = 80 yds and y '= 240 yds 14. The median price of a home in a certain neighborhood in 1986 was $80,000. By 1994, the median price had risen to $96,000. Assuming expo- nential growth, how long will it take fOr the median price to reach $120,000? 81n'1.5 ' a. ln1.2 yrs b. 20 yrs , 81ml} gc. lng yrs d. 16 yrs e. none of the above 15. Find all horizontal and vertical asymptotes of f (at) = 63:3 a. m=.3, y=0 b. sc=ln3,iy=00nly c.:1;-—f —1/3, y=0lon1y (1. 9321113, 3/: ~1/3 only ...=1n3,y;—1/3,o ' ' Elli 00W 1n 2 82$ 0 ~e$+1 dm 16. Evaluate a. 1+1}??— b.1113- C. ‘2' 2 (1’ 2+an 2 e. 1+ln§ .. 17. Let F(a:) = I: lit? dt. Find-F(3). .2. 5 :..§ 25 21:1 5 1115 9mm??? to: 01M:- 19. [55335315 dz: = a§.1n9 b. §lng c. 31n9» d. 3ln16 e. In!) _ em ) at a: = 1112. 633—1 20. Find the equation of the tangent line to f ( )= ln( a y=.——:B+lnx/§ b. y=~m+ln4 c. y=m+ln4 d. y=%m+ln\/2 =ln2 21. What is the total distance traveled by ,a particle traveling with velocity v(t)=-t?e1fromt='0tot=2? . .4 .2 .1. . 2 2, 3 .3 .ogpp-gn 2(.Bonus) I Wish I could get the following grade: (Hint there IS only one correct answer.) a.A ‘bB c.C d.D ~e.E My. 2E3 fill We 23. Which graph best representé f (w) = ill—‘5? a: MAC 2311 FINAL EXAM B SPRING 2008 A. Sign your scantron sheet in the white area on the back‘in ink. B. Write and encode in the spaces indicated: 1) Name (last name, first initial, middle initial) 2) UF ID number 3) Discussion Section Number _ C. Under “special codes”, encode the test ID number 5, 2. D. At the top right of your answer sheet, for “Test Form Code”, encode B. A o C ' D E V E. This test consists of 22 five-point multiple choice questions, and one five-point bonus question. The time allowed is 2 hours. F. When you are finished: ’ 1) Before turning in your test, check for transcribing errors. Any . , mistakes you leave in are there to stay. 2) You must turn in your scantron to your discussion leader. ‘Be pre— pared to show your picture ID with a) legible signature. 3) Answers will be posted on the MAC 2311 homepage. Problems 1 - 23 are Worth 5 points each, _ . 2a:__ 8 1. Flnd 11m$.,4 an)“; . a. 0' b. 2&4 0. 2:28" 8 d-% e4 6:7 2. If f(w) = figfii, find 1) and q Where p = limm_,3_ f(a:) and q = 1i11150_,_c>0 f(a:). I a.p=~—oo q=2 b. p: —1 (1:2 0- .P = +06 q = f2 'd- p .= -00 q = --2 e.p=+oo q=——oo . 3. Let tins: if a: > 7r/2 16(56): 8 g1 ifO < m < 7r/2 ‘ Si?“ if a: < 0 Lét P : links—47:12+~ f(33) V = limw—arO’I’ ft”) .a.p=+oo q=2 b.p_=+oo q=1 c.-p:f-oo q=2 d.p=—oo q=1 e.p=+oo q=0 4. Find the value of K which will make __ em+4 ifwél g($)—{m2+Km if$<1- continuous at :1: == 1. a. K.=e+3 b. K=e+2 c. K2953111- d.K=% 6. K24 H :1 ‘f’ CD 5. Evaluate 11mm.” (E l—l Dali-l O wh-J a. b. c. d. e. does not exist 7. What 1s the total distance traveled by a particle traveling with velocity v(t)=t2-1fromt=Otot=2? a.4 b.2 'c.% 2 d.§ e.3 8. Find fl (:1?) if f(m) = sin(tan2 :L'). a. f’ (:13) = 2 sin(tan a3) cos(sec2 a2) ‘ b. f’ (:0) = _cos(tan2 :13) secz a; 29: c. f’ (3:) = cos(tan2 m)2 tan a: sec (1. f’ (:3) == 2 sin(tan a3) cos(tan 93) sec2 :6 e. . f’(a3) = 23inmtanmse'c2 m + tan2 mcos a: 9. Find the slope of the tangent line to 51:231—233: 4f— 1 at (-— 1, 1). a. 6 10. Find the maximum and minimum values of f (cc) = m on [—1, 3]. a. O, —1 ' b. 2, 0. c. 2, 1 d. 2, —-1 e. 1, O 1 11. Find all horizontal and vertical asymptotes of f (:13) = em_3 a. a: = 3, y = O b. a: = ln3, y = 0 only c. a: :2 9-1/3, y = 0 only d. ac = ln3, y = -1/3 only e. a: = 1113, y = ——1/3,0 12. A rancher wants to enclose two rectangular areas near a river, one for sheep and the other for cattle. No fence is needed along the river. If she has 480 yards'of fencing available, What values oflcc and y will yield the largest total area he can enclose? a. a: :2 120 yds and y = 60 yds b. a: = 40 yds and y = 180 yds c. :1: = 80de and y := 120 yds d. :1: == 120 yds and y = 120 yds e. :1: = 80 yds and y = 240 yds 13. ConSider 'the function f(:c) .4: 3m +' 1:— -— 25. The graph of f(a:) is deCreasing and concave down on which of the following intervals? . a. (—5, 5) only b. (—oo,.—~5)U(O,5) c. (—5,0) only d. (—oo,——5)U(5,oo) ‘ e. (0, 5)"6nly 14.’ The median price of a home in a certain neighborhood in 1986 was $80,000. By 1994, the median price had risen to $96,000. Assuming expo- ‘ nential growth, how long will it take for the median price to reach $ 120,000? e. none of the above '15. The graph of f (w) = 3:265”2 has the following relative‘extrema: a. rel max: 0 rel min: ix/E b. rel maxi ix/E—i , rel min: 0 c. rel max: i1 rel min: ,0 d. relmax; O rel min: :l:1. e'. f (:13) has no relative extrema . 16. f3 “”24 den: 2 33—311: a. 31,;1I19 b. §In§ c. 31119 d. 31n16 ' e. 1119 17. Let F(:1:) 2 f3” if? dt. Find F’(3). w! CRIN m ~21n5 ln5 :0 9-”? ‘9‘? 01h?- N w—l 18. Find f’ (:13) Where f(m) =' 2”” . In 2 €23 0 e”’+1 d9” . 19. Evaluate 20. Find the equation of the tangent line to f (x) = ln( £1) at r13 = 1n 2. a. y = fiat + In x/i l). y = :13 + ln4 ' c. y = —a: +1114 (1. y, = 32—12: + ln\/§ e. y = ln2 , N103 21. An object travels 5(t) feet in t seconds, Where 3(t) == 75,2 + 2(t + 1)‘ . ‘ Find the acceleration of the object after t r: 3 seconds. ’ a. g—ft/sec2 . b. #141- ft/sec2 c. 12 ft/sec2 d. g- ft/sec2 e. 3:1 ft/sec2 22. (Bonus) I wish I could get the following grade: (Hint: there is only one correct answer.) a._A -"b.B- c.C d.D' 'e.E A 23. Which graph best represents f (:33) ...
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