MA 123 — Elem. CalculusEXAM 1Fall 201009/22/2010Name: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 answers on this page, but please do circle the letter of each 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:Total(out of 100 pts)1MA 123- Elem. CalculusEXAM 1Fall 201009/22/2010Please 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 347You may use the following formula for the derivative of a quadratic function.If p(x) = Ax2+ Bx + C, then p′(x) = 2Ax + B.2Multiple 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. Exactly one of the lines listed below is parallel to the line y = (−5/2) x + 7. Which one is it?Possibilities:(a) y = (2/5) x + 14(b) y = (−5/2) x + 13(c) y = (−2/5) x + 11(d) y = (5/2) x + 8(e) y = (−3/2) x + 72. Find the slope of the line in the graph shown below.-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4-3-2-1012345xyPossibilities:(a) −5/4(b) 4/5(c) −5(d) 5/4(e) −4/53. Mike is 8 years older than Nancy. In 9 years, the sum of their ages will be 56. How old is Nancynow?Possibilities:(a) 12(b) 13(c) 14(d) 15(e) 1634. Two trains start at the same train station. At noon, one train travels west at a velocity of 45 milesper h our and the other train travels east at a velocity of 55 miles per hour. How far apart are thetrains after two hours?Possibilities:(a) 200 mil es(b) 20 miles(c) 2475 mile s(d) 10 mile s(e) 100 miles5. Which of the following is the correct expression for the derivative g′(5)?Possibilities:(a)g(5) − g(5 + h)h(b)g(5 + h) − g(5)h(c) limh→0g(5) − g(5 + h)h(d) limh→0g(5 + h) − g(5)h(e) limh→0g(5 − h) − g(5)h6. Suppose−2x2+ 2x − 3 = A + B (x − 1) + C (x − 1)(x − 2).Find A.Possibilities:(a) −7(b) −6(c) −5(d) −4(e) −347. Computelimt→48 − t +t2t − 1Possibilities:(a) 9(b) 28/3(c) 29/3(d) 10(e) 31/38. Compute limt→4t2− 3t − 4t2− t − 12Possibilities:(a) 5/7(b) 6/7(c) 1(d) 8/7(e) 9/79. Compute limt→−2−|t + 2|t + 2Possibilities:(a) −2(b) −1(c) 0(d) 1(e) 2510. Find the average rate of change of f(x) = −3x − 1 on the interval [5, 8].Possibilities:(a) 3(b) 0(c) −9(d) −3(e) 911. 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) −3(b) −1(c) 0(d) 1(e) 412. Find the average rate of change of f(x) = 6x2− 1 from x = 5 to x = 5 + h.Possibilities:(a) −60h − 6h2(b) 60 + 6h(c) h(d) 60h + 6h2(e) −60 − 6h613. Let f (x) = 9x2− 6x − 7. Find the instantaneous rate of change of f(x) at x = −5.Possibilities:(a) 0(b) −96h + 9h2(c) −96 + 9h(d) −96(e) The instantaneous rate of change cannot be computed with the given information.14. Let f (x) = −5x2+ 7x + 7. Find a value c in the interval [−4, 2] so that the average rateof change of f(x) on [−4, 2] is equal to the instantaneous rate of change of f(x) at x = c.Possibilities:(a) −1(b) 0(c) 1(d) 2(e) 315. Solve the inequalityx2− 12x + 32 < 0Possibilities:(a) x < 4 or x > 8(b) x > 16(c) −8 < x < −4(d) x < −8 or x > −4(e) 4 < x < 8716. Find the value of m which makes f (x) differentiable everywhere, wheref(x) =(x2, if x ≤ 4;m (x − 4) + 16, if x > 4Possibilities:(a) 7(b) 8(c) 9(d) 10(e) 1117. A ball is thrown into the air. The height of the ball, measured in feet, t seconds later is given byh(t) = −16t2+ 64t. Find the instantaneous velocity of the ball at time t = 2.Possibilities:(a) −2 feet per second(b) −1 feet per second(c) 0 feet per second(d) 1 feet per second(e) 2 feet per second18. Let f (x) = 5x2− 3x − 5. Find an equation for the line through the points (1, f(1)) and (3, f(3)).Possibilities:(a) y + 3 = 17(x − 1)(b) y − 1 = 17(x + 3)(c) y − 1 = 17x − 3(d) y − 3 = 17(x + 1)(e) y = 17x − 14819. Let f (x) = 8x2− 4x − 2. Find an equation for the tangent li ne to the curve y = f(x) at the pointx = 2 .Possibilities:(a) y − 22 = 28(x − 2)(b) y − 2 = 28x + 22(c) y − 2 = 28(x − 22)(d) y = 28x − 78(e) y + 22 = 28(x + 2)20. Find the value of A which ma kes f (x) continuous everywhere, wheref(x) =(6x2, if x ≤ −3;−3x + A, if x > −3Possibilities:(a) 45(b) −3(c) 54(d) −9(e) No such value …