MA 123 — Elementary CalculusFINAL EXAMFall 200912/14/2009Name: 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 CalculusFINAL EXAMFall 200912/14/2009Please 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. Find the equation of the tangent line to the graph of the function y =9xat the point x = 3.Possibilities:(a) y = 3x + 3(b) y = 6x − 1(c) y = −x + 6(d) y = x − 6(e) y = −6x + 32. FindZ21(12x2+ 12x−2) dx.Possibilities:(a) 31(b) 32(c) 33(d) 34(e) 353. Suppose that f(x) =(12 − x2if x ≤ 42x − 3 if x > 4.Find limx→4+f(x).Possibilities:(a) 4(b) 5(c) 6(d) 7(e) 834. Suppose that f(x) = 2√x2+ 9. Findlimh→0f(4 + h) − f(4)h.Possibilities:(a) 1.2(b) 1.3(c) 1.4(d) 1.5(e) 1.65. What is the largest possible product you can form from two non-negative numbers x, y that satisfythe relation x2+ y = 48.Possibilities:(a) 122(b) 124(c) 126(d) 128(e) 13 06. Suppose that h(x) = f(x)3and that the equation of the tangent line to the graph of y = f(x) atx = 3 is given by y = 2 + 10(x − 3). Find h′(3).Possibilities:(a) 104(b) 108(c) 112(d) 116(e) 12 047. Two quantities F and G are functions of time. Suppose that F (t)G(t) = 12 for all values of t.When t = 4, suppose that F (4) = 2 and F′(4) = 6. Then find G′(4).Possibilities:(a) −15(b) −16(c) −17(d) −18(e) −198. Find f′(0) if f(x) =e4x2x2+ 4.Possibilities:(a) .2(b) .4(c) .6(d) .8(e) 19. Find the maximum value of the function f(x) =ln(x)xon the interval [1/2, 50].Possibilities:(a) 1/e(b) 1(c) e(d) e − 1(e) e − 2510. A bacteria culture starts with 6, 000 bacteria and the population quadruples after 5 hours. Find anexpression for the number P (t) of bacteria after t hours.Possibilities:(a) P (t) = 6000e(ln(5)/4)t(b) P (t) = 6 000e(ln(4)/5)t(c) P (t) = 60 00e(ln(4)+5)t(d) P (t) = 6000e(ln(5)+4)t(e) P (t) = 6000e5 ln(4)t11. Find the intervals where the function f(x) = x3+ 3x2− 45x + 7 is increasing.Possibilities:(a) (−∞, −5) and (3, ∞)(b) (−∞, 3) and (5, ∞)(c) (3, 5)(d) (−5, −3)(e) (−∞, −5) and (−3, ∞)12. Suppose that the derivative f′(x) = x3+ 3x2− 45x + 7. Find the intervals where the graph of thefunction y = f (x) is concave downward.Possibilities:(a) (−∞, −5) and (3, ∞)(b) (−∞, 3) and (5, ∞)(c) (−5, 3)(d) (−5, −3)(e) (−∞, −5) and (−3, ∞)613. Suppose that F (x) =Zx2√t2+ t + 1 dt. Find F′(6).Possibilities:(a)√43(b)√7(c)√43 −√7(d)√7 −√43(e) 1114. Find the limitlimn→∞4 + 8 + 12 + 16 + ··· + 4nn2.Possibilities:(a) 1(b) 1.5(c) 2(d) 2.5(e) 315. FindZ103x2ex3dx.Possibilities:(a) e + 2(b) e + 1(c) e(d) e − 1(e) 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 = lwh(b) Sphere V =43πr3(c) Cylinder V = πr2h(d) Cone V
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