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UK MA 123 - Exam

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MA 123 — Elementary CalculusFINAL EXAMSpring 201005/06/2010Name: 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 e xam is allowed.The exam consists of 15 multiple choice q uestions. Record your answers on this page by filling in thebox 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 e ach corre ct 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 CalculusFINAL EXAMSpring 2 01005/06/2010Please 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 M. Shaw MWF 12:00 pm - 12:50 pm, CP 153002 T. Chapman MWF 2:00 pm - 2:50 pm, CP 139003 P. Koester TR 12:30 pm - 1:45 pm, CP 153004 M. Shaw MWF 9:00 am- 9:50 am, BS 116005 P. Koester MWF 1:00 pm - 1:50 pm, CB 122D. Moore T 11:00 am - 12:15, CB 303006 P. Koester MWF 1:00 pm - 1:50 pm, CB 122J. Polly R 11:00 am - 12:15, DH 301007 P. Koester MWF 1:00 pm - 1:50 pm, CB 122D. Moore T 9:30 am - 10:45, CB 243008 P. Koester MWF 1:00 pm - 1:50 pm, CB 122J. Polly R 9:30 am - 10:45, CB 243009 D. Leep MWF 10:00 am - 10:50 am, CP 320A. Barra T 1:00 pm - 2:15, CP 397010 D. Leep MWF 10:00 am - 10:50 am, CP 320A. Barra R 1:00 pm - 2:15, CB 304011 D. Leep MWF 10:00 am - 10:50 am, CP 320A. Barra T 2:30 pm - 3:45, CP 246012 D. Leep MWF 10:00 am - 10:50 am, CP 320A. Barra R 2:30 pm - 3:45, CP 235013 A. Corso MWF 12:00 pm - 12:50 pm, CB 110401 D. Little TR 6:00 pm-7:15 pm, CB 339402 D. Little TR 7:30 pm-8:45 pm, CB 3392Multiple 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. f(x) has a single inflection point whose x coordinate is positive. Find the x coordinate of thisinflection point.f(x) = x4− 30x2+ 17x − 13Possibilities:(a)√3(b)√5(c)√7(d) 7(e) 52. Find the average rate of change of the function g(t) = t2− 3t + 4 on the interval [2, 4]Possibilities:(a) 6(b) 8(c) 4(d) 10(e) 33. A ball is thrown downward from the top of Patterson Office Tower. The height of the ball (in feet)t seconds after the ball is thrown is given byh(t) = −16t2− 15t + 240Find the instantaneous spe ed (in feet per second) of the ball after two seconds. (Note: Your answershould be a positive number since we are asking for speed, not velocity)Possibilities:(a) 76 fe et p er second(b) 74 feet per second(c) 70 feet per second(d) 72 feet per second(e) 79 fe et per second34. Find f0(20), provided thatf(x) = e3x2−4Possibilities:(a) 120 e1192(b) e1196(c) 596 e1196(d) 120 e1196(e) 120 e11955. Suppose g(4) = 4, g0(4) = −2 andf(x) =g(x)xFind f0(4).Possibilities:(a) −58(b) −78(c) −34(d) −54(e) −1186. Find the equation of the tangent line at x = 2 to the curve y = x2.Possibilities:(a) y = 6(x − 3) + 9(b) y = 10(x − 5) + 25(c) y = 4(x − 2) + 4(d) y = 4x + 8(e) y = 4(x − 2) − 447. Find the area of the largest rectangle which has one corner at the origin, opposite corner in thefirst qua drant and on the curve f(x) = 27−x2, and has sides parallel to the coordina te axes. (Hint:Let x denote the wid th of the rectangle. First, express the area of the rectangle in terms of x.)Possibilities:(a) 3(b) 54(c) 16(d) 128(e) 188. Suppose the derivative of f (x) is given by f0(x) = (x2− 9)(x2+ 5). Determine the largest intervalon which f(x) is decreasing.Possibilities:(a) (3, −∞)(b) (−∞, −3)(c) (−3, 3)(d) (−9, 9)(e) (9, ∞)9. Let P denote the pressure on a gas and V the volume of the gas. According to Boyle’s Law,P V = c where c is a constant. Currently, the pressure is 120 kPa, the volume is 40 cubic meters,and the pressure is increasing at rate of 15 kPa per minute. Find the rate at which the volume isdecreasing. (Note: Just give the numeric answer without a positive or negative sign.)Possibilities:(a) 5 cubic meters per minute(b) 2 cubic meters per minute(c) 6 cubic meters per minute(d) 7 cubic meters per minute(e) 3 cubic meters per minute510. Compute the limit:limn→∞5 + 10 + 15 + ··· + 5nn2Possibilities:(a)52(b) 0(c)32(d)72(e) Limit does not e xist11. Compute the integralZ419√x dxPossibilities:(a) 18(b) 42(c) 28(d) 63(e) 1412. Evaluate the integralZ2502x ex2dxPossibilities:(a) e625− 1(b) e529(c) 50e625− 50(d) e400− 1(e) 50e625− 1613. Find the derivative F0(x) given thatF (x) =Zx13t2dtPossibilities:(a) 5x4(b) 4x3(c) 6x(d) 3x2(e) x3− 114. Evaluate the integralZ5−4|t| dt(Hint: Drawing a graph will help)Possibilities:(a)292(b)172(c)232(d)132(e)41215. Compute the one-sided limitlimx→3+g(x)for the functiong(x) =x2− 1, x < 3;4, x = 3;−x + 6, x > 3Possibilities:(a) 4(b) 1(c) 8(d) 3(e) 27Some 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 = l wh(b) Sphere V =43πr3(c) Cylinder V = πr2h(d) Cone V


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UK MA 123 - Exam

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