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3 Pages

### 105F02Exam3

Course: MATH 105, Fall 2009
School: Oakland University
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Word Count: 650

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105 Math Exam 3 Fall 2002 Part I: Multiple Choice Questions (5 Points Each) 1. Find x at which the function f (x) = (x2 9)2 has the global maximum on the interval [1, 3]. (a) x = 0 (b) x = 1 (c) x = 3 (d) x = 3 (e) x = 2 2. Find the critical point(s) of the function (a) x = 1, 1 (b) none x . x2 +1 (c) x = 0 (d) x = 0, 1 (e) x = 0, 1 3. Consider the function f (x) = ex dened on (0, ). Which of the following...

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105 Math Exam 3 Fall 2002 Part I: Multiple Choice Questions (5 Points Each) 1. Find x at which the function f (x) = (x2 9)2 has the global maximum on the interval [1, 3]. (a) x = 0 (b) x = 1 (c) x = 3 (d) x = 3 (e) x = 2 2. Find the critical point(s) of the function (a) x = 1, 1 (b) none x . x2 +1 (c) x = 0 (d) x = 0, 1 (e) x = 0, 1 3. Consider the function f (x) = ex dened on (0, ). Which of the following is true? x (a) f has a global minimum at x = 1. (b) f has a global maximum at x = 1. (c) f is increasing on (0, ). (d) f is increasing on (0, 1) and decreasing on (1, ). (e) none of the other answers. 4. The indenite integral (a) 2x ln 2 2x dx equals (c) 2x+1 + c (Hint: 2x = e(ln 2)x ) (d) 2x ln 2 + c (e) ln (2x + c) +c (b) 2x + c 5. Find the inection point(s) of f (x) = xex . (a) x = 2 (d) x = 1 and x = 1 6. What substitution would enable you to nd the integral x2 dx x3 + 4 (a) u = x3 + 4 (b) u = x + 4 (c) u = ? x3 (d) u = x2 (e) u = x (b) x = 0 and x = 2 (c) x = 0 and x = 1 (e) none 7. Find the solution to the following initial value problem: dy = x3 3x2 , dx (a) 1 x4 x3 + 2 4 (e) x4 3x3 + 2 (b) 1 x4 x3 + 4 4 y (0) = 2 (c) 1 x4 x3 4 (d) x4 3x3 1 8. For the graphs labeled (I) through (IV), each of which is the graph of y = f (x) for some function. Identify any graphs satisfying the given conditions. There may be none or more than one. The function f (x) satises: f (x) > 0 for x < 2, f (1) > 0 and f (1) > 0. y y y y x x x x -2 (I) 1 (II) -2 1 -2 (III) 1 (IV) -2 1 (a) (I) only (d) (I), (II), and (IV) only (b) (IV) only (c) (I) and (IV) only (e) (II) and (IV) only 9. For the graphs labeled (I) through (IV), each of which is the graph of y = f (x) for some function. Identify any graphs satisfying the conditions. given There may be none or more than one. The function f (x) satises: f (x) > 0 on the intervals (, 1) and (2, ), f (x) < 0 on the interval (1, 2). y y y y x x x x -1 (I) 2 (II) -1 2 (III) -1 2 (IV) -1 2 (a) (II) only (d) (II) and (IV) only (b) (III) only (c) (I) and (IV) only (e) (II), (III), and (IV) only 10. If the acceleration of a particle is given by the formula a(t) = 4t + 1. Assuming that v (0) = 0, nd the velocity v (t) at t = 3. (a) 21 (b) 0 (c) 1 (d) 18 (e) none of the other answers 2 Part II: Partial Credit Questions (10 Points Each) Show all work and put your nal answer in the space provided. You will receive no credit if the answer is not in the space provided and no partial credit for a wrong answer if you do not show your work. 11. (i) Find the indenite integral et + 1 dt e2t . x x2 + 2dx . (ii) Find the indenite integral by substitution 12. (10 points) Solve the initial value problem y = e2x + 1, y (0) = 0. 13. (10 points) A farmer wants to build two holding pens next to the side of a barn (which wi...

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