MA 123 — Elementary CalculusSECOND MIDTERMFall 200910/21/2009Name: 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 CalculusSECOND MIDTERMFall 200910/21/2009Please 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 y = x3− x + 6 at x = 2. ThenPossibilities:(a) y = 11x − 10(b) y = 11x + 8(c) y = 10x + 11(d) y = 10x − 11(e) y = 11x + 122. Suppose that f(x) =4x − 7. Compute constants A, B, C such thatf(x + h) −f(x)h=A(x − 7)(x + Bh + C).Find A + B + C.Possibilities:(a) −8(b) −9(c) −10(d) −11(e) −123. Suppose thatf(x + h) − f(x)h=−2h(x + 4) − h2h(x + h + 4)2(x + 4)2.Find the slope m of the tangent line to the graph of y = f(x) at x = −1.(Suggestion: First compute f′(x).)Possibilities:(a) 2/2 7(b) −2/81(c) 0(d) −2/27(e) None of the above34. Assume that f(x) = 2ex3+4x.Find the equation of the tangent line to the graph of y = f(x) at x = 2.Possibilities:(a) y = e16+ 16e16(x − 2)(b) y = 2e16+ 32e16(x − 2)(c) y = 2e16+ 16e16(x − 2)(d) y = 2e16+ 2e16(x − 2)(e) y = 2e16+ e16(x − 2)5. Suppose that F (x) = g(h(x)).If h(3) = 5, h′(3) = 7, g(3) = 2, g′(3) = −1, g(5) = 6, and g′(5) = 4, then find F′(3).Possibilities:(a) −5(b) −4(c) 42(d) 35(e) 286. Suppose that f(x) =5x − 1x2+ 2x. Find f′(2).Possibilities:(a) 5/5(b) −7/32(c) 14/64(d) −10/32(e) 18/6447. Suppose that f(x) =√x2− 5−3. Find f′(3).Possibilities:(a) 9/2(b) 3/64(c) −3/64(d) −9/32(e) −9/28. Suppose that the e quation of the tangent line to the graph of y = f(x) at x = 5 is given by theequation y = 8 + 4(x −5). Find f(5) + f′(5).Possibilities:(a) 10(b) 11(c) 12(d) 13(e) 149. If f(x) = (x3+ 4x2+ 1)3/2, then find f′(2).Possibilities:(a) 190(b) 195(c) 200(d) 205(e) 21 0510. A bacteria culture starts with 8000 bacteria and the population quadruples after 4 hours. If weexpress the number of bacteria as P (t) = P0ert, then find r.Possibilities:(a) (1/4) ln 4(b) 2 ln 4(c) (1/2) ln 4(d) 4 ln 4(e) ln 411. If g(x) = ln(x3+ 2x + 4), then find g′(3).Possibilities:(a) 4/3 7(b) 37/29(c) 4/29(d) 29/37(e) 29/ ln 3712. The half-life of a radioactive substance is 20 years. Suppose that we have a 400 gram sample.How many grams will remain after 60 years?Possibilities:(a) 100 /3(b) 200/3(c) 50(d) 30(e) 25613. Let m denote the minimum value and let M denote the maximum value of f(x) = x3−9 x2+15x+5on the interval [0, 6]. Find M + m.Possibilities:(a) −7(b) −8(c) −9(d) −10(e) −1114. Suppose that g(x) = x2−4x + 9. Find a number c such that g′(c) equals the average rate of changeof g(x) on the interval [1, 9].Possibilities:(a) 2(b) 3(c) 4(d) 5(e) 615. Find the maximum value of h(x) = |x − 4| + 12 on the interval [−10, 9].Possibilities:(a) 22(b) 23(c) 24(d) 25(e)
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