Math 132, Spring 2009 - Exam 2NAME: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 question 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 p oints, 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. 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 = −122. ComputeZ422x3− 2x2− 1x2− x.(a) 12 + ln(2/3).(b) 16 + ln(4).(c) 16 + ln(4) + ln(3).(d) 16 + ln(4/3).(e) 16 + ln(3/4).(f) ∞.(g) −∞.(h)32.33. 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)C(x+1)5(d)Dx(e)Ex+Fx2+1(f)Gx+Hx2−1(g)Jx+1(h)K(x+1)344. Use the Trapezoidal Rule with n = 4 to approximateR20√x2+ x dx.(a) 0.41(b) 0.86(c) 1.27(d) 1.55(e) 2.31(f) 2.72(g) 3.33(h) 3.5455. Use Simpson’s Rule with n = 4 to approximateR20√x2+ x dx.(a) 0.86(b) 1.32(c) 2.75(d) 3.38(e) 3.45(f) 3.54(g) 4.27(h) 4.3466. Find the minimum number of subintervals needed toapproximateR10ex2dx with an error less than 10−4,when using the Trapezoidal Rule.(a) 4(b) 50(c) 63(d) 117(e) 189(f) 224(g) 451(h) 100377. EvaluateR∞1x−11/10dx.(a) 2(b) 10(c) 25(d) 110(e) 1100(f) 1250(g) ∞(h) −∞88. EvaluateZ∞21ln(x)dx(a) Converges, by direct comparison with compari-son function1x2.(b) Diverges, by direct comparison with the compar-ison function1x2.(c) Converges, by direct comparison with the com-parison function ex.(d) Diverges, by direct comparison with the compar-ison function ex.(e) Converges, by direct comparison with the com-parison function1x.(f) Diverges, by direct comparison with the compar-ison function1x.(g) Converges, by direct comparison with the com-parison function e−x.(h) Diverges, by direct comparison with the compar-ison function e−x.99. EvaluateZ∞1dx√e2x− x2(a) Converges, by limit comparison with the compar-ison function1x.(b) Diverges, by limit comparison with the compari-son function1x.(c) Converges, by limit comparison with the compar-ison function1ex.(d) Diverges, by limit comparison with the compari-son function1ex.(e) Converges, by direct comparison with compari-son function1x.(f) Diverges, by direct comparison with the compar-ison function1x.(g) Converges, by direct comparison with the com-parison function1ex.(h) Diverges, by direct comparison with the compar-ison function1ex.1010. EvaluateZ20dxx − 1(a) Diverges to ∞.(b) Diverges to −∞.(c) Diverges but not to −∞ or ∞.(d) 0(e) 1(f) −1(g) 2(h) −21111. The region between the curve y = 2√x, 0 ≤ x ≤ 1,and the x-axis is revolved about the x-axis to gener-ate a solid. Compute the volume of this solid.(a) π/2(b) π(c) 2π(d) 5π/2(e) 5π(f) π2(g) π2/2(h) 16π/151212. Find the volume of the solid generated by revolvingthe region bounded by y = |x| and y = 1 about thex-axis.(a) 4π/3(b) π(c) 2π(d) 5π/2(e) 5π(f) π2(g) π2/2(h) 6.31313. Find the volume of the solid generated by revolvingthe region between x = y2+ 1 and the line x = 2about the line x = 2.(a) π/2(b) π(c) 2π(d) 5π/2(e) 5π(f) π2(g) π2/2(h) 16π/151414. Find the length of the curve given byy = x3/2, 0 ≤ x ≤ 4/3(a) 2/3(b) 4/3(c) 8/3(d) 8/27(e) 9/4(f) 13/4(g) 56/27(h) 128/2715Name: Student ID:15. Use the shell method to find the volume of the solidgenerated by revolving the region bounded byy = 1 + x2/4, 0 ≤ x ≤ 1, and the x-axisabout the line x = −1.16Name: Student ID:16. Find the length of the curve given byx = cos3t, y = sin3t, 0 ≤ t ≤ π/217Name: Student ID:18Name: Student
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