MA 123 — Elem. CalculusEXAM 4Fall 201012/15/2010Name:Sec.:Do not remove this answer page — you will turn in the entire exam. You have two hours to do thisexam. No books or notes may be used. You may use a graphing calculator during the exam, but NOcalculator with a Computer Algebra System (CAS) or a QWERTY keyboard is permitted. Absolutelyno cell phone use during the exam is allowed.The exam consists of multiple choice questions. Record your answers on this page. For each multiplechoice question, you will need to fill in the box corresponding to the correct answer. For example, if (b)is correct, you must writeabcdeDo not circle a nswers on this page, but please circle the letter of ea ch correct response in the body ofthe exam. It is your responsibility to make it CLEA R which response has been chosen. You will not getcredit unless the correct answer has been marked on both this page and in the body of the exam.GOOD LUCK!1.abcde2.abcde3.abcde4.abcde5.abcde6.abcde7.abcde8.abcde9.abcde10.abcde11.abcde12.abcde13.abcde14.abcde15.abcde16.abcde17.abcde18.abcde19.abcde20.abcdeFor grading use:NumberCorrect(out of 20 problems)Total(out of 100 points)1MA 123- Elem. CalculusEXAM 4Fall 201012/15/2010Please make sure to list the correct section number on the front page of your exam. In case you forgotyour section number, consult the following table. If you are enrolled in a lecture with recitation, thenyour section number is determined by your recitation time and location.Section # Instructor Lectures001 T. Chapman MWF 8:00 am - 8:50 am, CB 118002 D. Leep MWF 12:00 pm - 12:50 pm, KAS 213003 M. Shaw TR 8:00 am - 9:15 am, CP 155004 J. Schmidt TR 12:30 am- 1:45 am, CP 155005 M. Music T 3:30 pm - 4:45 pm, CP 345006 M. Music R 3:30 pm - 4:45 pm, CP 208007 W. Robinson T 3:30 pm - 4:45 pm, CP 208008 W. Robinson R 3:30 pm - 4:45 pm, CB 204009 M. Music T 12:30 pm - 1:45 pm, NURS 214010 W. Robinson R 12:30 pm - 1:45 pm, NURS 504011 S. Taylor T 9:30 am - 10:45 am, BE 248012 S. Taylor R 9:30 am - 10:45 am, CB 214013 B. Fox T 9:30 am - 10:45 am, MMRB 243014 B. Fox T 9:30 am - 10:45 am, FB B3015 C. Taylor T 11:00 am - 12:15 pm, CB 347016 B. Fox T 11:00 am - 12:15 pm, CB 243017 C. Taylor T 2:00 pm - 3:15 pm, NURS 511018 C. Taylor R 2:00 pm - 3:15 pm, DH 323019 G. Tiser T 2:00 pm - 3:15 pm, CB 213020 S. Taylor R 2:00 pm - 3:15 pm, FB B8021 G. Tiser T 12:30 pm - 1:45 pm, FPAT 255022 G. Tiser R 12:30 pm - 1:45 pm, DH 323401 S. Foege TR 6:00 pm-7:15 pm, CB 347402 S. Foege TR 7:30 pm-8:45 pm, CB 3472Multiple Choice QuestionsShow all your work on the page where the question appears.Clearly mark your answer both on the cover page on this examand in the corresponding questions that follow.1. Let y = (2x2+ 14)3/2. Find the equation of the tangent line at x = 1 .Possibilities:(a) y = 20x + 44(b) y = 21x + 43(c) y = 22x + 42(d) y = 23x + 41(e) y = 24x + 402. Let f(x) = 6x2+ 52x − 2. For what value of x is the slope of the tangent line to the graph ofy = f(x) at x equal to 4?Possibilities:(a) −5(b) −4(c) −3(d) −2(e) −13. The number of a bacteria in a culture doubles every 15 hours. How many hours will it take before7 times the original amount is present?Possibilities:(a) 15/7(b) 15 ln (2)/ ln (7)(c) 15 ln (7)/ ln (2)(d) 105/2(e) 15/234. Evaluate the limit as n tends to infinity. Note that you will have to use the summation formulasto first simplify.limn→∞1nnXk=15kn2If the limit tends to ±∞, select “Limit d oes not e xist”.Possibilities:(a) 25/6(b) 0(c) 5/3(d) 25/3(e) Limit does n ot exist5. Find the second derivative, f′′(x), wheref(x) = ex3Possibilities:(a) x3ex3−1(b) x3(x3− 1) ex3−2(c) 6 x ex2+ 6 x ex(d) 6 x ex3+ 9 x4ex3(e) 3x2ex36. Compute limt→4t2− 2t − 8t − 4Possibilities:(a) 4(b) 5(c) 6(d) 7(e) 847. The graph of y = f(x) is shown below. Compute limx→1−f(x).-5-4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345xyPossibilities:(a) −4(b) −2(c) −1(d) 0(e) 18. Evaluate the sum42 + 48 + 54 + 60 + . . . + 264 + 270Possibilities:(a) 6042(b) 6210(c) 6084(d) 6120(e) 10149. Evaluate the integralZ904t3+ 2t2+4√tdtPossibilities:(a) 7071(b) 7072(c) 7073(d) 7074(e) 7075510. Evaluate the integralZ3−3|t| dtPossibilities:(a) 9(b) 10(c) 11(d) 12(e) 1311. Use the Fundamental Theorem of Calculus to compute the derivative of F (x), ifF (x) =Zx94√tdtYour answer should be an expression involving the variable x.Possibilities:(a) 4/√x(b) 2√x − 6(c) (4/√x) − (4/3)(d) 4x−3/2− (4/27)(e) 8√x − 2412. A rock is thrown down from a cliff with an initial speed of 10 feet per second. The speed of therock after t seconds is s(t) = 32 t + 10 . If the object lands after 4 seconds, d etermine the heightof the cliff.Possibilities:(a) The cliff is 216 feet high.(b) The cliff is 296 feet high.(c) The cliff is 128 feet high.(d) The cliff is 256 feet high.(e) The cliff is 10 feet high.613. Evaluate the integralZ1268t − 5dtPossibilities:(a) −96/7(b) 96/7(c) 8 ln (12) −8 ln (6)(d) 8 ln (7)(e) 714. Suppose f (−2) = 7, f′(−2) = −3, g(−2) = −6, and g′(−2) = −9. Find K′(−2), given thatK(x) =f(x)g(x)Possibilities:(a) 1/3(b) −27/2(c) −9/4(d) 27/2(e) 9/415. Estimate the area under the graph of f(x) = 5x2for x between 0 and 6. Use a partition that consistsof 3 equa l subintervals of [0, 6] and use the right endpoint of each subinterval as the sample point.Possibilities:(a) 675(b) 200(c) 1080(d) 135(e) 560716. Suppose you want to find the shortest distance between the point (5, 0) on the x-axis and a pointon the parabola y =√8 − x. Solving which of the equations below will help?(5, 0)f(x) =√8 − xbPossibilities:(a) Solve D = 0 , where D =qx2+ (√8 − x − 5)2, for x ≤ 8(b) Solve D = 0 , where D =p(x − 5)2+ 8 − x, for x ≤ 8(c) Solve D′= 0 , where D =qx2+ (√8 − x − 5)2, for x ≤ 8(d) Solve D′= 0 , where D =p(x − 5)2+ 8 − x, for x ≤ 8(e) Solve D′= 0 , where D =q(x − 5)2+√8 − x, for x ≤ 817. The area of a circle is increasing at a rate of 3 squa re inches per minute. Determine the rate a twhich the radius of the circle is increasing when the radius of the circle is 4Possibilities:(a)38 πinches per minute(b)118 πinches per minute(c)198 πinches per minute(d)278 πinches per minute(e)358 πinches per minute818. Assume that f(x) is a differentiable function for all values of x. Furthermore, assume thatf′(x) > 0 on the intervals (−∞, −1), (1, 7), and (9, ∞)f′(x) < 0 on the intervals (−1, 1) and (7, 9)The local