Math 132, Spring 2011 - Exam 1NAME:STUDENT ID NUMBER:This exam contains sixteen questions. The first fourteenare multiple choice questions and count for five pointseach. There is no partial credit on these questions, soread each questio n carefully, check your arithmeticand make sure that you have marked the answer you in-tended to mark. The last two questions, which are eachworth fifteen points, require written answers, and somepartial credit might be given. However, no credit will begiven for information that is not germane to the problemat hand. Please make sure to write your name and stu-dent ID number on the pages that include your answersto the last two questions. In fact, you will get onepoint on each of these two questions for writingyour name and ID number legibly.11. Compute2Z11x2dx(a) 2/3(b) 3/2(c) −1/2(d) 1/4(e) −3/4(f) 3/4(g) 0(h) 1/222. Find an antiderivative of f(t) =1√t.(a) −12√t+ C(b)12√t+ C(c) −12t3/2+ C(d) −12t3/2(e) −2√t + 5(f) 2√t + 5(g)12√t(h) −12√t33. Suppose f is a function such thatf(0) = 10, f0(0) = 22, f00(0) = 2f(4) = 1, f0(4) = 20, f00(4) = 30Compute4Z0f00(t) dt(a) −9(b) −2(c) 28(d) 12(e) 10(f) 1(g) 8(h) 1844. Compute4Z13r − 1√rdr(a) 12(b) 3(c) 2(d)23(e)12(f) 14(g) −3(h) −1255. A table of values for an increasing function g is shown.x 10 15 20 25 30g(x) -4 -2 0 1 11Use this table to find lower and upper estimates for30Z10g(x) dx(a) −4, 10(b) −2, 20(c) 0, 30(d) 6, 100(e) −6, 100(f) −5, 70(g) −6, 70(h) −25, 5066. Supposeg(y) =yZ2t10sint dtCompute g0(y)(a) y10siny(b) y10cosy(c) −y10cosy(d) 9y siny + y10cosy(e) 9y siny − y10cosy(f) 9y siny − y10cosy − 2(g) 9y siny + y10cosy − 4sin2(h) 9y siny − y10cosy + C77. Supposeh(x) =πZx√1 + sec t dtCompute h0(x).(a) −π(b) π(c)√1 + sec t(d)√1 + sec x(e) −√1 + sec t(f) −√1 + sec x(g)√1 + sec π −√1 + sec x(h)√1 + sec π −√1 + sec x + C88. ComputeZdxx lnx(a) cos(ex) + C(b) ecos x+ C(c) x sin(ex) + C(d) −ln |x| + C(e) ln |x| + C(f)1ln(x)+ C(g) ln |ln x| + C(h)1x+ C99. Compute−1Z0z2(1 + 2z3)5dz(a)16(b) −16(c)136(d) −136(e)13(f) −118(g) 0(h) −191010. EvaluateeZ19x2(ln x) dx(a) 0(b) 1 + 2e3(c)12(d) e − 1(e) 9e3(f) 3e2(g) −2 − e2(h) −23+ e1111. ComputeZπ40√1 + cos4x dx(a)π4(b) 0(c) 1(d)√22(e)√2(f) 2(g) 4(h) 0.251212. Expandx+4(x+1)2by partial fractions.(a)1x+1+x+3(x+1)2(b)2x+1+x+2(x+1)2(c)3x+1+x+1(x+1)2(d)4x+1+x(x+1)2(e)1x+1+3(x+1)2(f)3x+1(g)3(x+1)2(h) impossible since undefined at x = −11313. Which term does NOT appear in the partial fractionsexpansion ofx8+ 3x7− 20x5+ 13x3− x2+ x − 7x2(x + 1)4(x4− 1)(a)Ax2(b)B(x+1)4(c)Gx+Hx2−1(d)C(x+1)5(e)Dx(f)Ex+Fx2+1(g)Jx+1(h)K(x+1)31414. Compute1Z01(√x2+ 1)3dx(a) 0(b) π/3(c) π/4(d) π/2(e)√2/2(f) −√2/2(g) 1/2(h) −1/215Name: Student ID:15. EvaluateZetsin(2t) dtShow your work.16Name: Student ID:16. Computelimn→∞nXi=121 + (i/n)2.1nShow all work.17Name: Student ID:18Name: Student ID:19Name: Student
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