MA 123 — Elementary CalculusTHIRD MIDTERMFALL 200811/19/2008Name: 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 CalculusTHIRD MIDTERMFALL 200811/19/2008Name:Please 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 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. Two trains leave a station at the same time. One travels north on a track at 1 20 mph. The secondtravels east on a track at 50 miles per hour. How fast are they traveling away from one another inmiles per hour when the northbound train is 120 miles from the station?Possibilities:(a) 120(b) 125(c) 128.4(d) 130(e) 13 2 .62. An expanding rectangle has its length always equal to twice its width. The area is increasing at arate of 64 square feet per minute. At what rate is the width increasing when the width is 2 feet?Possibilities:(a) 10(b) 8(c) 6(d) 5(e) 43. Find the point (x0, y0) in the first quadrant that lies on the hyperbola y2− x2= 5 and is closest tothe point A(6, 0). Then (x0, y0) isxy0•APossibilities:(a) (1,√6)(b) (2, 3)(c) (2.5,√11.25)(d) (3,√14)(e) (4,√21)34. Suppose that the sum of x and y is 9, x and y both positive. What is the value of x that gives thelargest possible value of x2y?Possibilities:(a) 6(b)√6(c) 8(d)√8(e) 45. Evaluate the sum6Xk=2(k2+ k).Possibilities:(a) 100(b) 102(c) 106(d) 108(e) 11 06. Estimate the area under the graph of y = 3x2for x between 1 and 5. Use a partition thatconsists of 4 equal subintervals of [1, 5] and use the right endpoint of each subinterval as a samplepoint.xy0 1 2 3 4 5Possibilities:(a) 162(b) 164(c) 166(d) 168(e) 17 047. Suppose that the integralZ61f(x) dx is estimated by the sumNXk=1f(a + k ∆x) · ∆x. Theterms in the sum equal areas of rectangles obtained by using right endpoints of the subintervalsof length ∆x as sample points. If N = 50, then what is ∆x?Possibilities:(a) .05(b) .1(c) .5(d) 1(e) Cannot be d etermined8. Suppose that the integralZ522f(x) dx is e stimated by the sumNXk=1f(a + k∆x) · ∆x. Theterms in the sum equal areas of rectangles obtained by using right endpoints of the subintervalsof length ∆x a s sample points. If f(x) =1xand N = 50 , then find the area of the second rectangle.Possibilities:(a) 1/1 6(b) 1/9(c) 1/8(d) 1/4(e) 1/29. Suppose that the integralZ104√x dx is estimated by the sumNXk=1p(a + k∆x) ·∆x, where∆x = .2 and N = 30. The terms in the sum equal areas of rectangles obtained by using rightendpoints of the subintervals of length ∆x as sample points. What is a?Possibilities:(a) 2(b) 3(c) 4(d) 5(e) 6510. Suppose that the derivative of f(x) is given by f′(x) = x2− 5x + 6. Then the graph of f(x) isconcave upward on the following interval(s).Possibilities:(a) (−∞, 2) and (3, ∞)(b) (2, 3)(c) (−∞, 2.5)(d) (2.5, ∞)(e) f (x) is not concave downward on any interval.11. Let f(x) = xe2x. Then f is incre asing on the following interval.Possibilities:(a) (−∞, −1/2)(b) (−1/2, ∞)(c) (−∞, 1/2)(d) (1/2, ∞)(e) (−∞, 0)12. Find a local extre me point of f(x) =ln xx.Possibilities:(a) (1, 0) is a local minimum point.(b) (1, 0) is a local maximum point.(c) (e, 1 /e) is a local maximum point.(d) (e, 1/e) is a local minimum point.(e) f (x) has no local extreme points.613. Evaluate the integralZ40(12 − 2x) dxxy0 4 612y = 12 − 2xPossibilities:(a) 40(b) 48(c) 32(d) 24(e) 3614. Evaluate the sum30Xk=1(6k2− 2k).Possibilities:(a) 55, 900(b) 55, 800(c) 55, 600(d) 55, 400(e) 55, 30015. Evaluate the sum 6 + 9 + 12 + 15 + 18 + 21 + ·· · + 600.Possibilities:(a) 60, 287(b) 60, 290(c) 60, 293(d) 60, 297(e) 60, 3007Some 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