MA 123 — Elementary CalculusTHIRD MIDTERMFall 200911/18/2009Name: Sec.:Do not remove this answer page — you will return the whole exam. You will be allowed two hoursto complete this test. No books or notes may be used. You may use a graphing calculator during theexam, but NO calculator with a Computer Algebra System (C AS) or a QWERTY keyboard is permitted.Absolutely no cell phone use during the exam is allowed.The exam consists of 15 multiple choice q uestions. Record your answers on this page by filling in thebox corre sponding to the correct an swer. For e xample, 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 CLEAR 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.abcdeFor grading use:number ofcorrect problems(out of 15)Total(out of 100 pts)1MA 123 — Elementary CalculusTHIRD MIDTERMFall 200911/18/2009Please make sure to list the correct section number on the front page of your exam.In case you forgot your section number, consult the following table:Section # Instructor Lectures001 P. Koester MWF 8:00 am - 8:50 am, CP 153002 P. Koester MWF 12:00 - 12:50 pm, BS 107003 T. Chapman TR 8:00 a m - 9:15 am, C P 1 53004 M. Shaw MWF 2:00 pm- 2:50 pm, BS 107005 M. Shaw MWF 1:00 pm-1:50 pm, BS 107006-009 D. Leep MWF 10:00 am - 10:50 am, CB 114401 D. Little TR 6:00 p m-7: 15 pm, CB 347402 D. Little TR 7:30 p m-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. Suppose that the derivative f′(x) = 1 + 2x2+ 3x4. Find the value of x in the interval [−5, 7] wheref(x) takes its minimum.Possibilities:(a) x = −5(b) x = −1(c) x = 0(d) x = 3(e) x = 72. Find the x-coordinate of the inflection point of the function f(x) = (2x − 3)e−x.Possibilities:(a) 5/2(b) 3(c) 7/2(d) 4(e) 9/23. Suppose that the derivative f′(x) = 2x3− 3x2− 72x + 5. Then the graph of y = f(x) is concaveupward on the following intervals.Possibilities:(a) (−∞, −3) and (4, ∞)(b) (−∞, −4) and (3, ∞)(c) (−3, 4)(d) (−4, 3)(e) (0, ∞)34. Assume that f(x) is a differentiable function for all values of x. Suppose that f′(x) > 0 for x < −6,1 < x < 4 , and 10 < x < ∞. Suppose also that f′(x) < 0 for −6 < x < 1 and 4 < x < 10. The localminimum points of f(x) occur atPossibilities:(a) x = 1 and x = 4(b) x = −6 and x = 10(c) x = −6, x = 1, x = 4, and x = 10(d) x = 1 and x = 10(e) x = −6 and x = 45. What is the largest possible product you can form from two non-negative numbers x, y that satisfythe relation 6x + y = 11.Possibilities:(a) 122 /24(b) 121/24(c) 5(d) 119/24(e) 11 8 /246. Find the area of the largest rectangle with one corner at the origin, the opposite corner in the firstquadrant on the graph of the parabola f(x) = 96 − 2x2, and sides parallel to the axes.Possibilities:(a) 256(b) 260(c) 264(d) 268(e) 27 247. A ladder 20 feet long rests against a vertical wall. If the bottom of the ladder slides away fromthe wall at a rate of 6 feet/sec, how fast is the top of the ladder sliding down the wall when thebottom of the ladder is 16 feet from the wa ll? Give your answer in feet per second. (The answeris a positive number because we use the phrase “sliding down”)Possibilities:(a) 6(b) 7(c) 8(d) 9(e) 51 08. A conical salt spread er is spreading salt at a rate of 4 cubic feet per minute. The diameter of thebase of the cone is 6 feet and the height of the cone is 8 feet. How fast is the height of the salt in thespreader decreasing when the height of the salt in the spreader (measured from the vertex of thecone upward) is 3 feet? Give your answer in feet per minute. (The answer is a positive numberbecause we use the word “decreasing”)Possibilities:(a) 64/ 81π(b) 96/81π(c) 128/81π(d) 256/81π(e) 51 2 /81π9. Estimate the a rea under the graph of f(x) = 18 − 4x2on the interval [0, 2] by d ividing the intervalinto four equal parts. Use the left endpoint of each interval as a sample point.Possibilities:(a) 25(b) 26(c) 27(d) 28(e) 29510. Suppose that the integralZ832x2dx is estimated by the sum40Xk=1[A+B(k∆x)+C(k∆x)2]· ∆x. Theterms in the sum equal areas of rectangles obtained by using right endpoints of the subintervalsof length ∆x as sample points. What is the value of A + B + 2C?Possibilities:(a) 30(b) 31(c) 32(d) 33(e) 3411. Suppose that the integralZ2812f(x) dx is estimated by the sumNXk=1f(12 + k∆x) · ∆x. Theterms in the sum equal areas of rectangles obtained by using right endpoints of the subintervalsof length ∆x as sample points. If N = 400 equal subintervals are used, what is the value of ∆x?Possibilities:(a) 0.01(b) 0.02(c) 0.04(d) 0.05(e) 0.0812. Suppose that the integralZ277f(x) dx is estimated by the sumNXk=1f(7 + k∆x) · ∆x. Theterms in the sum equal areas of rectangles obtained by using right endpoints of the subintervalsof length ∆x as sample points. If f (x) = x2and N = 40, then find the area of the 6threctangle.Possibilities:(a) 48(b) 50(c) 52(d) 54(e) 56613. Evaluate the sum22Xk=5(4 + 3k).Possibilities:(a) 801(b) 802(c) 803(d) 804(e) 80 514. Evaluate the sum30 + 36 + 42 + 48 + 54 + · · · + 270.Possibilities:(a) 6135(b) 6140(c) 6145(d) 6150(e) 61 5515. Evaluate the sum12Xk=1(2k2+ 5k + 3).Possibilities:(a) 1725(b) 1726(c) 1727(d) 1728(e) 17 297Some Formulas1. Summation formulas:nXk=1k =n(n + 1)2nXk=1k2=n(n + 1)(2n + 1)62. Areas:(a) Triangle A =bh2(b) Circle A = πr2(c) Rectangle A = lw(d) Trapezoid A =b1+ b22h3. Volumes:(a) Rectangular Solid V = lwh(b) Sphere V =43πr3(c) Cylinder V = πr2h(d) Cone V