MATH 152 Spring 2009 COMMON EXAM II VERSION A LAST NAME First name print INSTRUCTOR SECTION NUMBER UIN SEAT NUMBER DIRECTIONS 1 The use of a calculator laptop or computer is prohibited 2 In Part 1 Problems 1 10 mark the correct choice on your ScanTron using a No 2 pencil For your own records also record your choices on your exam 3 In Part 2 Problems 11 15 present your solutions in the space provided Show all your work neatly and concisely and clearly indicate your final answer You will be graded not merely on the final answer but also on the quality and correctness of the work leading up to it 4 Be sure to write your name section number and version letter of the exam on the ScanTron form THE AGGIE CODE OF HONOR An Aggie does not lie cheat or steal or tolerate those who do Signature DO NOT WRITE BELOW Question Points Awarded Points 1 10 40 11 12 12 12 13 12 14 12 15 12 100 1 PART I Multiple Choice 1 4 pts Find the length of the curve y a b c d e x3 from the point 0 0 to the point 4 8 3 10 10 1 2 4 9 2 10 10 1 3 8 10 10 1 27 2 3 2 4 pts The improper integral Z xe 3x dx 0 a Converges to 9 1 b Converges to 9 c Converges to 0 d Converges to 1 9 e Diverges 2 3 4 pts Z 1 2 x2 1 dx x2 x a 1 3 ln 2 2 ln 3 b 1 3 ln 2 2 ln 3 c 2 3 ln 2 2 ln 3 d 2 3 ln 2 2 ln 3 e None of the above 4 4 pts Find the surface area obtained by rotating the curve y 4 x2 0 x 2 around the y axis a b c d e 5 5 1 6 4 17 17 1 3 4 5 5 1 3 6 17 17 1 6 3 K b a 3 where K max f x for a x b what is the smallest 2 12n Z 3 value of n so that the approximation Tn The trapezoidal rule with n subintervals to the integral ln x dx is 5 4 pts Using the error bound formula ET accurate to within 1 1 2400 a n 40 b n 20 c n 60 d n 30 e n 70 6 4 pts A group of calculus teachers were sitting around an odd shaped pool see figure below The widths in meters of this pool were measured at 2 meter intervals as indicated Use Simpson s rule with n 4 to approximate the area of this pool 1 5 m 2m 3m a 22 square meters 22 square meters b 3 17 square meters c 3 17 d square meters 2 44 square meters e 3 4 Z dx x e5x 1 Z a Diverges by comparison to 7 4 pts The integral b c d e dx x 1 Z dx Converges by comparison to e5x 1 Z dx Diverges by comparison to e5x 1 Z dx Converges by comparison to x 1 Converges to 0 8 4 pts Given du e2t u and u 0 1 find u 1 dt 1 1 a u 1 ln e2 e 2 2 b u 1 ln e 1 c u 1 ln 2e2 e 2 1 1 d u 1 ln e2 e 2 2 e u 1 ln e 1 5 9 4 pts Find the surface area obtained by rotating the curve x sin t y cos t 0 t around the x axis 3 a b c d e 3 2 3 2 2 2 10 4 pts The curve x e8y 0 y 1 is revolved around the x axis Which of the following integrals gives the resulting surface area r Z 1 1 a 2 y 1 e16y dy 64 0 r Z 1 1 b 2 e8y 1 e16y dy 64 0 Z 1 p 2 y 1 64e16y dy c 0 Z 1 p 1 64e16y dy 0 r Z 1 2 1 8y 1 e8y dy e 2 e 64 0 d 2 e8y 6 PART II WORK OUT Directions Present your solutions in the space provided Show all your work neatly and concisely and Box your final answer You will be graded not merely on the final answer but also on the quality and correctness of the work leading up to it 11 12 pts A tank is full of oil and has the shape below Find the hydrostatic force against one end of the semi circular tank Note the weight density of oil is g 9000 Newton s per cubic meter 1m semicircle 10 m 7 12 A tank contains 250 liters of pure water Brine that contains 0 01 kg of salt per liter enters the tank at a rate of 20 liters per minute The solution is kept mixed and drains from the tank at a rate of 20 liters per minute How much salt is in the tank after t minutes 8 13 12 pts Find Z x 2 dx x2 x2 1 9 14 12 pts Find a general solution to the differential equation x 10 dy x ln x 2 y dx 15 12 pts Find the centriod of the region bounded by y x and y x3 Simplify your answer End of Exam 11
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