Student Print Section Last First Middle Student Sign Student ID Instructor MATH 152 Fall 2007 Common Exam 1 Test Form A Instructions You may not use notes books calculator or computer For Dept use Only 1 10 50 11 10 12 10 after 90 minutes and may not be returned 13 10 Part II is work out Show all your work Partial credit will be given 14 10 15 10 Part I is multiple choice There is no partial credit Mark the Scantron with a 2 pencil For your own records also circle your choices in this exam Scantrons will be collected THE AGGIE CODE OF HONOR An Aggie does not lie cheat or steal or tolerate those who do TOTAL 1 Part I Multiple Choice 5 points each There is no partial credit 1 Compute 1 0 xe x 2 1 dx a 1 e b c d e 2 1 e 1 2 1 e2 2 1 e 2 1 2 1 e 2 e 2 2 Compute 2 0 x cos x dx a 1 2 b 1 c 2 2 d 1 e 1 3 Find the area below the parabola y 3x x 2 above the x axis a 1 b c d e 2 9 2 27 2 81 2 10 3 2 4 Find the average value of f x e 3x on the interval 0 2 a 1 e 6 1 b c d e 5 3 1 e6 3 1 e 6 1 6 1 e6 6 e 6 1 The region shown at the right is bounded above by y sin x and below by the x axis It is rotated about the x axis Find the volume swept out y 1 0 0 5 0 0 0 1 2 3 x 2 a 2 b 2 2 c 2 d 2 e 4 6 The region in Problem 5 is rotated about the the line x 1 Which formula gives the volume swept out a b c d e 0 1 sin x 2 1 0 2 x 1 sin x dx 0 x 1 sin x dx 1 2 x sin x dx 0 1 sin x 2 dx dx 3 7 The region bounded by the curves x 1 y 1 and y 4 x is rotated about the x axis Find the volume swept out a b c d e 8 8 ln 4 15 15 8 ln 4 12 9 8 A solid has a base which is a circle of radius 2 and has cross sections perpendicular to the y axis which are isosceles right triangles with a leg on the base Find the volume of the solid a 32 b c d e 3 64 3 128 3 16 3 32 3 4 9 A certain spring is at rest when its mass is at x 0 It requires 24 Joules of work to stretch it from x 0 to x 4 meters What is the force required to maintain the mass at 4 meters a b c d e 48 Newtons 18 Newtons 12 Newtons 6 Newtons 24 Newtons 2 10 Find the partial fraction expansion for f x 5x 3 x 12 x 4x a 1 3x2 2 b c d e x 2 x 1 x 2 x 3 x x 4 x 3 x2 4 2x 3 x2 4 3x 1 x2 4 2x 1 x2 4 5 Part II Work Out 10 points each Show all your work Partial credit will be given 11 Compute a 5 points cos 3 d b 5 points x 3 ln x dx 6 12 Find the area between the cubic y x 3 x 2 and the line y 2x 13 A water tower is made by rotating the curve y x 4 about the y axis where x and y are in meters If the tower is filled with water of density 1000 kg m 3 up to height y 25 m how much work is done to pump all the water out a faucet at height 30 m Assume the acceleration of gravity is g 9 8 m sec 2 You may give your answer as a multiple of g 7 1 x2 dx 4 x 2 3 2 4 x 4 dx x 2 16 14 Compute 0 15 Compute 0 8
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