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UK MA 123 - MA 123— Elementary Calculus FIRST MIDTERM

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MA 123 — Elementary CalculusFIRST MIDTERMFALL 200809/24/2008Name: 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 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 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 CalculusFIRST MIDTERMFALL 200809/24/2008Please 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 A. Corso MWF 8:00am-8:50am, CP 153002 J. Robbins MWF 12:00pm-12:50pm, CP 1 53003 T. Chapman TR 8:00am-9:15am, B S 116004 M. Anton MWF 12:00pm-12:50pm, BS 116005 D. Leep MWF 3:00pm-3:50pm, CP 153401 P. Cooley TR 6:00pm-7:15pm, CB 347402 P. Cooley TR 7:30pm-8:45pm, 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. John leaves at 9:00 am and drives from Lexington to Ashland arriving a t 11:00 am. He stops fortwo hours since his girlfriend Mary is not yet ready. Then they drive together from Ashland toColumbus arriving at Columbus after a three-hour drive. The distance from Le xington to Ashlandis 110 miles and the distance from Ashland to Columbus is 130 miles. Find the average velocity ofJohn’s car in miles per hour for the entire trip (including the two hour stop) correct to two decimalplaces.Possibilities:(a) 33.8 1(b) 33.42(c) 35.00(d) 34.29(e) 34.4 72. Let f (x) = 2x2− 3x. Find the average rate of change of f (x) from x = 3 to x = 3 + h.Possibilities:(a) 9 − h(b) 9 + h(c) 9(d) 9 − 2h(e) 9 + 2h3. Suppose that h(t) =2t. Find the average rate of change of h(t) from t = 5 to t = 10.Possibilities:(a) −.05(b) −.04(c) .05(d) .04(e) .0234. Let g(x) = x2+ 4x + 5 . Find a value of c between 1 and 10 such that the average rate of change ofg(x) from x = 1 to x = 10 is equal to the instantaneous rate of g(x) at x = c.Possibilities:(a) 4.75(b) 5.0(c) 5.25(d) 5.5(e) 5.755. Computelimx→3x2− 7x + 12x − 3.Possibilities:(a) 0(b) 1(c) −1(d) 2(e) Does not exist6. Let f (x) =(x2+ 8x + 15 if x ≤ 24x + 7 if x > 2.Find limx→2+f(x).Possibilities:(a) 15(b) 20(c) 30(d) 35(e) Does not exist47. Compute limh→0(h + 4)2− 16h.Possibilities:(a) 4(b) 5(c) 6(d) 7(e) 88. Find the slope of the tangent line to the graph of f (x) = 3x2− 7 x + 4 at x = 2.Possibilities:(a) 5(b) 6(c) 7(d) 8(e) 99. If h(t) represents the height of an object a bove ground level at time t and h(t) is given byh(t) = −16t2+ 96t + 1,find the height of the object at the time when the velocity is zero.Possibilities:(a) 144(b) 145(c) 148(d) 150(e) 16 0510. Compute limx→3−|4x − 12|x − 3.Possibilities:(a) 4(b) −4(c) 0(d) Cannot be determined(e) Does not exist11. Find A and B such that the e quation of the line through (1 , 3) and (2 , 7) can be written asy = A + B(x − 2).Possibilities:(a) A = 4 and B = 7(b) A = 7 and B = 4(c) A = 3 and B = 1(d) A = 7 and B = 2(e) This is not p ossible.12. What is the value of x such that the slope of the tangent line to the graph of f(x) = x2− 10x + 14is 6?Possibilities:(a) There is no such x.(b) 6(c) 7(d) 8(e) 9613. Consider the function f(x) =(2x2+ 3 if x ≤ 33x + B if x > 3.Find a value of B such that f (x) is continuous at x = 3.Possibilities:(a) 6(b) 9(c) 12(d) 15(e) There is no such value of B.14. The values of x satisfying the inequality x2+ 5x − 24 < 0 arePossibilities:(a) x < −8 and x > 3(b) x < 8 and x > −3(c) Cannot be determined(d) −3 < x < 8(e) −8 < x < 315. Computelimx→02x2− 3x + 4x+5x − 4x.Possibilities:(a) 5(b) 4(c) 3(d) 2(e)


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UK MA 123 - MA 123— Elementary Calculus FIRST MIDTERM

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