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UK MA 123 - MA 123 — Elem. Calculus

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MA 123 — Elem. CalculusEXAM 3Fall 201011/17/2010Name:Sec.:Do not remove this answer page — you will turn in the entire exam. You have two hours to do thisexam. No books or notes may be used. You may use a graphing calculator during the exam, but NOcalculator with a Computer Algebra System (CAS) or a QWERTY keyboard is permitted. Absolutelyno cell phone use during the exam is allowed.The exam consists of multiple choice questions. Record your answers on this page. For each multiplechoice question, you will need to fill in the box corresponding to the correct answer. For example, if (b)is correct, you must writeabcdeDo not circle a nswers on this page, but please circle the letter of ea ch correct response in the body ofthe exam. It is your responsibility to make it CLEA R 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.abcde16.abcde17.abcde18.abcde19.abcde20.abcdeFor grading use:NumberCorrect(out of 20 problems)Total(out of 100 points)1MA 123- Elem. CalculusEXAM 3Fall 201011/17/2010Please make sure to list the correct section number on the front page of your exam. In case you forgotyour section number, consult the following table. If you are enrolled in a lecture with recitation, thenyour section number is determined by your recitation time and location.Section # Instructor Lectures001 T. Chapman MWF 8:00 am - 8:50 am, CB 118002 D. Leep MWF 12:00 pm - 12:50 pm, KAS 213003 M. Shaw TR 8:00 am - 9:15 am, CP 155004 J. Schmidt TR 12:30 am- 1:45 am, CP 155005 M. Music T 3:30 pm - 4:45 pm, CP 345006 M. Music R 3:30 pm - 4:45 pm, CP 208007 W. Robinson T 3:30 pm - 4:45 pm, CP 208008 W. Robinson R 3:30 pm - 4:45 pm, CB 204009 M. Music T 12:30 pm - 1:45 pm, NURS 214010 W. Robinson R 12:30 pm - 1:45 pm, NURS 504011 S. Taylor T 9:30 am - 10:45 am, BE 248012 S. Taylor R 9:30 am - 10:45 am, CB 214013 B. Fox T 9:30 am - 10:45 am, MMRB 243014 B. Fox T 9:30 am - 10:45 am, FB B3015 C. Taylor T 11:00 am - 12:15 pm, CB 347016 B. Fox T 11:00 am - 12:15 pm, CB 243017 C. Taylor T 2:00 pm - 3:15 pm, NURS 511018 C. Taylor R 2:00 pm - 3:15 pm, DH 323019 G. Tiser T 2:00 pm - 3:15 pm, CB 213020 S. Taylor R 2:00 pm - 3:15 pm, FB B8021 G. Tiser T 12:30 pm - 1:45 pm, FPAT 255022 G. Tiser R 12:30 pm - 1:45 pm, DH 323401 S. Foege TR 6:00 pm-7:15 pm, CB 347402 S. Foege TR 7:30 pm-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) > 0 for all x in the interval (2, 8). Which statement isdefinitely true?Possibilities:(a) f(x) is decreasing on the interval (2, 8).(b) f(x) is concave down on the interval (2, 8).(c) f(x) is concave up on the interval (2, 8).(d) f(x) is increasing on the interval (2, 8).(e) The graph of f (x) must be above the x-axis on the interval (2, 8).2. Suppose that the derivative of g(t) is g′(t) = (t − 5) (t − 9) (t − 13) . Find the value of t in theinterval [5, 13] where g(t) has its maximum.Possibilities:(a) t = 9(b) t = 7(c) t = 6(d) t = 5(e) t = 133. Find the largest interval on which f(x) = x4− 6x3− 60x2− x + 5 is concave down.Possibilities:(a) (−2, 7)(b) (−2, 6)(c) (−2, 5)(d) (−2, 8)(e) (−2, 4)34. Determine the x-coordinate of the inflection point off(x) = x3− 12x2− 4x + 5Possibilities:(a) 4(b) 5(c) 6(d) 7(e) 85. Suppose the first and second derivatives of f(x) are given byf′(x) = (1 − 3x) e−3xand f′′(x) = 3 (3x − 2) e−3xFind the largest interval on which f(x) is concave down.Possibilities:(a) (−∞, 2/3)(b) (1/3, ∞)(c) (2/3, ∞)(d) (3, ∞)(e) (−∞, 3)6. Two positive real numbers, x and y, satisfy xy = 18. What is the minimum value of theexpression 2x + y?Possibilities:(a) 10(b) 11(c) 12(d) 13(e) 1447. Find the area of the largest rectangle with one corner at the origin, the opposite corner in the firstquadrant on the graph of the curve f(x) = 12 − x2. (See the graph, but the graph is not to scale.)Possibilities:(a) 14(b) 15(c) 16(d) 17(e) 188. A rectangle is to be constructed with 6 vertical partitions (i.e., 7 vertical walls and 2 horizontalwalls) as in the figure below. The rectangle is to be constructed with 35 00 feet of material. Let xdenote the length of the horizontal wall and y the length of the vertical wall. Which optimizationproblem needs to be solved in order to determine how to enclose the largest area?y| {z }xPossibilities:(a) Maximize A = xy, given that 2x + 6y = 3500.(b) Maximize A = 2x + 5y, given that xy = 3500.(c) Maximize A = 2 x + 6y, given that xy = 3500.(d) Maximize A = xy, given that 2x + 7y = 3500.(e) Maximize A = 2x + 7y, given that xy = 3500.59. A train is traveling over a bridge at 48 miles per hour. A man on the train is walking toward theback of the train at 4 miles per hour. How fa st is the man traveling across the bridge in miles perhour?Possibilities:(a) 42(b) 44(c) 46(d) 48(e) 5010. A ladder of length 10 feet rests against a wall. The bottom of the ladder is being pulled away fromthe wall at a rate of 3 feet pe r second. How fast is the top of the lad d er sliding down the wallwhen the bottom of the ladder is 8 feet from the wall? (Just give the numeric value of the answer.Do not worry about the p lus or min us sign.)Possibilities:(a) 2 feet per second(b) 3 feet per second(c) 4 feet per second(d) 5 feet per second(e) 6 feet per second11. A stock is increasing at a rate of 16 dollars per share per year. An investor is buying stock at a rateof 14 shares per year. How fast is the value of the investor’s stock growing when the price of thestock is 53 dollars p er share and the investor owns 40 shares of the stock? (Hint: Write down anexpression for the total value, V, of the stock owned by the investor.)Possibilities:(a) $1382 per year.(b) $224 per year.(c) $1408 per year.(d) $2120 per year.(e) $640 per year.612. Estimate the a rea under the graph of f (x) = x2+ 5x for x between 0 and 2. Use a partition thatconsists of 4 equal subintervals of [0, 2] and use the left endpoint of each subinterval as the samplepoint.Possibilities:(a) 37/4(b) 633/50(c) 65/4(d) 6(e) 2013. Suppose that the integralZ5238f(x) dx is estimated by the sumNXk=1f(38 + k ∆x) · ∆x. Theterms in the sum equal areas of rectangles


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