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 clear will be part of the grade Useful Formulas n X i i 1 n X i2 i 1 n X i 1 3 n n 1 2 n n 1 2n 1 6 i n n 1 2 2 Area Circle Radius r r2 Area Ellipse With Semi Major Axis a Semi Minor Axis b ab Math 132 Exam 1 Page 2 of 11 1 Let f x be the function satisfying f 00 x sin x ex f 0 0 2 and f 0 0 Find f 2 A e 2 2 1 B e 2 C 2e 2 2 D e 2 2 E e 2 1 F e 2 2 G e 2 1 2 Suppose you know the following about a function f x Z 4 f x dx 4 1 8 Z f x dx 3 2 8 Z f x dx 4 1 Z Find 2 2f x 6 dx 1 A 5 B 3 C 0 D 2 E 4 F 6 G 8 H None of the above Math 132 Exam 1 Page 3 of 11 3 Suppose f x f 0 x and f 00 x are all continuous functions and you know the following additional information about f x f 2 4 f 6 12 f 0 2 5 f 0 6 11 f 00 2 6 f 00 6 10 Z If possible find 6 f 00 x dx 2 A 0 B 2 C 4 D 6 E 8 F 10 G 12 Z H We do not have enough information to determine 2 Z 4 Compute 6 1 x 4 dx 2 A 0 B 2 C 4 D 6 E 8 F 10 G 12 H None of the above 6 f 00 x dx Math 132 Exam 1 Z Page 4 of 11 2 sin5 x cos x dx 5 Find 0 A 0 B 1 6 C 16 D 1 3 E 13 F 1 G 1 H None of the above Z 6 Let u ln x and rewrite the following integral in the variable u Z A u e3u du Z B u du Z C u e2u du Z D u2 ln u du Z E u2 eu du Z eu ln u du F Z G u3 ln u du Z H u2 e2u du x2 ln x dx Math 132 Exam 1 Z 3 7 Compute 36 4x2 dx 0 A 4 5 B 4 5 C 9 D 9 E 18 F 18 G 36 H None of the above 8 A function f x and a number b satisfy the question Z x f t dt 24x 3 3 4 t b What is b A 0 B 1 C 2 D 3 E 4 F ln 3 G ln 8 H It is not possible to determine b Page 5 of 11 Math 132 Exam 1 Page 6 of 11 9 Let f x x2 1 Compute L4 over the interval 1 3 L4 is the Riemann sum using left endpoints as sample points with 4 subdivisions A 0 B 2 75 C 3 D 5 E 9 F 10 G 12 5 H 18 10 Identify the definite integral that is equal to the limit of Riemann Sums 8 n X 4 4i lim 1 n n n i 1 Z 5 x 1 7 dx A 0 Z 8 x 4 7 dx B 4 Z 6 x8 dx C 2 Z 4 x8 dx D 0 Z 5 x 1 8 dx E 2 Z F 5 x8 dx 1 G None of the above Math 132 Z 11 Exam 1 Page 7 of 11 3 3x2 2 dx lim Rn where Rn is the right hand Riemann sum Find Rn n 0 A B C D E F G H 27 n 1 2n 1 6 2n2 n 9 n 1 2n 1 6 2n2 2 18 n 1 2 2 n n 81 n 1 2n 1 2 2n2 27 n 1 2n 1 6 2n2 18 n 1 15 3n 9 n 1 2 3 2n2 None of the above Z x3 12 Let F x ln 3t 5 dt Find F 0 x sin x2 A ln 3x3 5 B ln 3 sin x2 5 C ln 3x3 5 ln 3 sin x2 5 D 3x2 ln 3x3 5 E 2x cos x2 ln 3 sin x2 5 F 3x2 ln 3x3 5 2x cos x2 ln 3 sin x2 5 G 3x2 ln 3x3 5 2x cos x2 ln 3 sin x2 5 H 0 Math 132 Exam 1 Z x 13 If g x 13 t2 Page 8 of 11 12 dt what is g 0 1 2t A 0 B 1 C 3 D 4 E 6 F 10 G 12 H None of the above 14 Find the area of the region enclosed by the graphs of f x 1 x2 and g x x2 1 A 2 B C D E 1 2 3 2 3 5 4 3 F 4 G 8 3 H None of the above Math 132 Exam 1 Page 9 of 11 15 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 0 B C D 5 6 5 3 5 2 E 3 F 5 G 6 H 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 B C D E F G 3 5 8 3 2 3 3 4 7 4 33 5 5 3 H None of the above Math 132 Exam 1 Page 10 of 11 Name ID Discussion Section Letter You can find your discussion section on the front of your exam book Written 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 must show all of your steps and your work must be easy to follow Z e x a dx e x 2 4 Z b 0 e 1 x3 dx x2 1 Math 132 Exam 1 Page 11 of 11 Name ID Discussion Section Letter You can find your discussion section on the front of your exam book Written Problem You will be graded on the readability of your work Use the back of this sheet if necessary 18 Let f x 6 and g x 5 x x a Graph …
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