c©Texas A&M Dept. of Mathematics, March 22, 2004 1 MATH 152 Spring 2004 Exam 2 Test Form A NAME LAST FIRST ID# INSTRUCTOR’S NAME SECTION # INSTRUCTIONS In Part I (Problems 1{9), mark the correct choice on your SCANTRON sheet using a #2 pencil. Use the back of the rst page for scratch work. For your own records, record your responses on your exam (which will be returned to you). No calculators. In Part II (Problems 10{15), write all solutions in the space provided. Use the back of the rst page for scratch work, but all work to be graded must be shown in the space provided. CLEARLY INDICATE YOUR FINAL ANSWER. No calculators. Multiple choice Q10 Q11 Q12 Q13 Q14 Q15 Total c©Texas A&M Dept. of Mathematics, March 22, 2004 2 Part I. MULTIPLE CHOICE, NO PARTIAL CREDIT, NO CALCULATORS (5 points each) 1. The term A (x +2) 2 appears in the partial fraction form of x 2 +2x+1 (x+2) 3 .FindA. a.) 2 b.) −1 c.) 0 d.) 1 e.) −2 2. Suppose f satis es f(x) > 0, f 0 (x) > 0, and f 00 (x) < 0 for all x in [a; b]. Let I = R b a f(x) dx,andletT 4 ,L 4 ,andR 4 be the Trapezoidal Rule, left endpoint approx- imation, and right endpoint approximation, respectively, to I using four subintervals. Which, if any, of the following statements are true? (i) T 4 I; (ii) T 4 I; (iii) L 4 I; (iv) L 4 I; (v)R 4 I; (vi)R 4 I: a.) (i), (iii), and (vi)only b.) (ii), (iv), and (v)only c.) (i), (iv), and (v)only d.) (iii), and (vi)only e.) Can’t be determined from the given information 3. Which of the following statements is true about Z 1 0 e −x p x dx? a.) It is divergent because e −x p x 1 p x in (0; 1) and Z 1 0 1 p x dx is divergent. b.) It is convergent because e −x p x x p x in (0; 1) and Z 1 0 x p x dx is convergent. c.) It is divergent because x p x e −x p x in (0; 1) and Z 1 0 x p x dx is divergent. d.) It is convergent because e −x p x 1 p x in (0; 1) and Z 1 0 1 p x dx is convergent. e.) It is convergent because e −x e −x p x in (0; 1) and Z 1 0 e −x dx is convergent. c©Texas A&M Dept. of Mathematics, March 22, 2004 3 4. Solve the initial value problem dy dx = xy 2 ;y(0) = 1. If the solution is denoted by y(x), then y(1) =? a.) 1 b.) 0 c.) 2 d.) 1/2 e.) 3/2 5. An integrating factor for y 0 sin x = −y cos x + x +1; 0