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WUSTL MATH 132 - math132-fall2016-Exam1

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Math 132 Exam 1 Fall 2016• 16 multiple choice questions worth 4.5 points each.• 2 hand graded questions worth 14 points each.• Exam covers sections 4.9 through 6.2• No calculators!• For the multiple choice questions, mark your answer on the answer card.• Show all your work for the written problems. Your ability to make your solution clearwill be part of the grade.Useful FormulasnXi=1i =n(n + 1)2nXi=1i2=n(n + 1)(2n + 1)6nXi=1i3=n(n + 1)22(Area Circle Radius r) = πr2(Area Ellipse With Semi-Major Axis a, Semi-Minor Axis b) = πabMath 132 Exam 1 Page 2 of 111. Let f(x) be the function satisfying f00(x) = sin x + ex, f0(0) = 2, and f(0) = 0. Findf(π/2).A. eπ/2+ π/2 − 1B. eπ/2+ πC. 2eπ/2+ π/2D. eπ+ π/2 − 2E. eπ/2− 1F. eπ/2+ π − 2G. eπ/2− π + 12. Suppose you know the following about a function f(x):•Z41f(x) dx = 4•Z82f(x) dx = −3•Z81f(x) dx = 4FindZ212f(x) − 6dx.A. −5B. −3C. 0D. 2E. 4F. 6G. 8H. None of the aboveMath 132 Exam 1 Page 3 of 113. Suppose f(x), f0(x), and f00(x) are all continuous functions and you know the followingadditional information about f(x):f(2) = 4 f(6) = 12f0(2) = 5 f0(6) = 11f00(2) = 6 f00(6) = 10If possible, findZ62f00(x) dx.A. 0B. 2C. 4D. 6E. 8F. 10G. 12H. We do not have enough information to determineZ62f00(x) dx.4. ComputeZ621 + |x − 4|dx.A. 0B. 2C. 4D. 6E. 8F. 10G. 12H. None of the aboveMath 132 Exam 1 Page 4 of 115. FindZπ/20sin5x cos x dx.A. 0B.16C. −16D.13E. −13F. 1G. −1H. None of the above.6. Let u = ln x and rewrite the following integral in the variable u:Zx2ln x dx.A.Zu e3uduB.Zu duC.Zu e2uduD.Zu2ln u duE.Zu2euduF.Zeuln u duG.Zu3ln u duH.Zu2e2uduMath 132 Exam 1 Page 5 of 117. ComputeZ30√36 − 4x2dx.A. 4.5B. 4.5πC. 9D. 9πE. 18F. 18πG. 36H. None of the above8. A function f(x) and a number b satisfy the question3 +Zxbf(t)t4dt = 24x−3.What is b?A. 0B. 1C. 2D. 3E. 4F. ln 3G. ln 8H. It is not possible to determine b.Math 132 Exam 1 Page 6 of 119. Let f(x) = x2+ 1. Compute L4over the interval [−1, 3].(L4is the Riemann sum using left endpoints as sample points, with 4 subdivisions.)A. 0B. 2.75C. 3D. 5E. 9F. 10G. 12.5H. 1810. Identify the definite integral that is equal to the limit of Riemann Sums:limn→∞nXi=11 +4in84nA.Z50(x + 1)7dxB.Z84(x + 4)7dxC.Z62x8dxD.Z40x8dxE.Z52(x + 1)8dxF.Z51x8dxG. None of the aboveMath 132 Exam 1 Page 7 of 1111.Z30(3x2− 2) dx = limn→∞Rn, where Rnis the right hand Riemann sum. Find Rn.A.27(n + 1)(2n + 1)2n2−6nB.9(n + 1)(2n + 1)2n2− 6C.18(n + 1)2n2−2nD.81(n + 1)(2n + 1)2n2− 2E.27(n + 1)(2n + 1)2n2− 6F.18(n + 1)3n+ 15G.9(n + 1)22n2− 3H. None of the above12. Let F (x) =Zx3sin(x2)ln(3t + 5)dt. Find F0(x).A. ln(3x3+ 5)B. ln(3 sin(x2) + 5)C. ln(3x3+ 5) − ln(3 sin(x2) + 5)D. 3x2ln(3x3+ 5)E. 2x cos(x2) ln(3 sin(x2) + 5)F. 3x2ln(3x3+ 5) − 2x cos(x2) ln(3 sin(x2) + 5)G. 3x2ln(3x3+ 5) + 2x cos x2ln(3 sin(x2) + 5)H. 0Math 132 Exam 1 Page 8 of 1113. If g(x) =Zx1312t2+ 2tdt, what is g0(1)?A. 0B. 1C. 3D. 4E. 6F. 10G. 12H. None of the above14. Find the area of the region enclosed by the graphs of f(x) = 1 − x2and g(x) = x2− 1.A. 2B.12C.32D.35E.43F. 4G.83H. None of the aboveMath 132 Exam 1 Page 9 of 1115. A solid is formed with a base that is a triangle with vertices at (0, 0), (5, 0) and (0, 1).Cross sections of this solid, perpendicular to the x axis are squares.Find the volume of the solid.A. 0B.56C.53D.52E. 3F. 5G. 6H. ∞16. Let R be the region in the plane enclosed by y = x3, y = 0, and x = 1.Find the volume of the solid formed by rotating R about the axis x = 2.A.3π5B.8π3C.2π3D.3π4E.7π4F.33π5G.5π3H. None of the aboveMath 132 Exam 1 Page 10 of 11Name:ID:Discussion Section Letter:You can find your discussion section on the front of your exam bookWritten Problem. You will be graded on the readability of your work.Use the back of this sheet, if necessary.17. Compute the following integrals using the substitution method. For full credit, you mustshow all of your steps and your work must be easy to follow.(a)Ze−x(e−x+ 2)4dx.(b)Z√e−10x3x2+ 1dx.Math 132 Exam 1 Page 11 of 11Name:ID:Discussion Section Letter:You can find your discussion section on the front of your exam bookWritten Problem. You will be graded on the readability of your work.Use the back of this sheet, if necessary.18. Let f(x) =6xand g(x) = 5 − x.(a) Graph the region enclosed by the curves y = f(x) and y = g(x). Be sure to labelthe curves and any intersection points.(b) Find the volume of the solid obtained by rotating the region from (a) about


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WUSTL MATH 132 - math132-fall2016-Exam1

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