MA 123 — Elem. CalculusFIRST MIDTERMSPRING 200702/07/2007Name: 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 15 multiple choice questions. Record your answers on this page by filling in thebox corresponding to the correct answer. 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:Total(out of 100 pts)1MA 123 — Elem. CalculusFIRST MIDTERMSPRING 200702/07/2007Name:Sec.:Please make sure to list the correct section number on the front page of your exam and on this page.In case you forgot your section number, consult the following table:Section # Instructor Lectures001 J. Robbins MWF 12:00pm-12:50pm, BS 107002 P. Perry MWF 2:00pm-2:50pm, CB 118003 J. Robbins TR 3:30pm-4:45pm, CB 337004 S. Speakman MW 7:30pm-8:45pm, CB 339004 N. Kirby TR 6:00pm-7:15pm, CB 3392Multiple 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. If P (s) = s2+ 1 and R(t) = t − 2, then P (R(x)) =Possibilities:(a) x2− 4x + 5(b) x2+ 4x + 3(c) x2− 1(d) x2+ 5(e) (x2+ 1)(x − 2)2. What is the average rate of change of g(s) = s2− 4 as s changes from 1 to 1 + h?Possibilities:(a) 6 + 3h(b) 2 + h(c) 4 + 2h(d) 2(e) h3. The inequality x2+ 2x − 15 ≤ 0 can be rewritten in the formPossibilities:(a) x ≤ −3 or x ≥ 5(b) −5 ≤ x ≤ 3(c) x ≥152(d) x ≤ −5 or x ≥ 3(e) −3 ≤ x ≤ 534. If the equation of the line through the points (3, 0) and (2, 1) is written asy = A + B(x − 2),thenPossibilities:(a) A = 1 and B = −1(b) A = 3 and B = −1(c) A = −1 and B = 3(d) A = −1 and B = 1(e) A = 5 and B = −15. A rectangular solid has edges of lengths 4 ft, 5 ft, and 8 ft. Suppose we double the length of twoof the sides. What is the volume of the new rectangular solid?Possibilities:(a) 80 ft3(b) 160 ft3(c) 320 ft3(d) 640 ft3(e) 1280 ft36. Find the limitlimt→2t2− 4t − 2Possibilities:(a) Does not exist(b) 2(c) 4(d) 6(e) 847. If we simplify the expressiona5b8− a4b7a(ab2)2to the form aPbQ− aRbS, then R =Possibilities:(a) 0(b) 1(c) 2(d) 3(e) 48. In this problem you may use the fact that if f(x) = Ax2+ Bx + C then f0(x) = 2Ax + B.Suppose X(t) represents the height of an object above the ground at time t, where the height ismeasured in feet and the time t is measured in seconds. IfX(t) = −16t2+ 48t + 144,what is the speed of the object at time t = 0?Possibilities:(a) 48 feet per second(b) 144 miles per hour(c) 32 furlongs per fortnight(d) 64 feet per second(e) 96 feet per second9. Suppose the parabola given by the equation y = A + B(x + 1) + C(x + 1)(x − 2) contains the points(−1, 3), (2, 6), and (3, 7). What is the value of B?Possibilities:(a) −2(b) −1(c) 0(d) 1(e) 2510. Suppose thatf(x) =(A + x x < 21 + x2x ≥ 2Find a value of A such that the function f (x) is continuous at the point x = 2.Possibilities:(a) A = 8(b) A = 1(c) A = 2(d) A = 3(e) A = 011. If a(t) = t − 4, find a function b(t) such that a(b(t)) = t.Possibilities:(a) b(t) = t(b) b(t) = 4(c) b(t) = t − 4(d) b(t) = t + 4(e) b(t) = 4 − t12. A train travels from city A to city B. It leaves city A at 10:30 AM and arrives at city B at 1:30 PM.The distance between the cities is 150 miles. What was the average speed of the train in miles perhour?Possibilities:(a) 60 miles per hour(b) 150 miles per hour(c) 50 miles per hour(d) 75 miles per hour(e) 130 miles per hour613. In this problem you may use the fact that if f (x) = Ax2+ Bx + C then f0(x) = 2Ax + B.Suppose that G(x) = x2+ x − 2. For what value of x is the tangent line to the graph of y = G(x)parallel to the x-axis?Possibilities:(a) x = −1(b) x = 0(c) x = 2(d) x = 1/2(e) x = −1/214. Suppose H(t) = t2+ 5t + 1. Find the limitlimt→2H(t)Possibilities:(a) 15(b) 1(c) 9(d) 6(e) 2t + 515. Find the limitlimh→0−|4h|hHint: Evaluate the quotient for some negative values of h close to 0.Possibilities:(a) 0(b) 2(c) −2(d) 4(e)