Math 132 Final Exam Spring 2008 1 This exam contains 20 multiple choice questions Each question is worth 5 points 1 Find the arc length of y x3 1 12 x over the interval 1 3 Hint Use the identity 1 y 0 2 x2 4 x 2 2 A 8 13 B 13 12 C 7 9 D 5 12 E 2 5 F 13 6 G 17 6 H 15 12 I 5 6 J 17 12 Math 132 Final Exam Spring 2008 2 2 Which of the following integrals correctly represents the surface area of revolution of y ex about the x axis over the interval 0 1 A B C D E F G H I J R1 u 1 u2 du 0 R1 1 u2 du 0 Re 1 u 1 u2 du Re 1 1 u2 du R1 2 0 u 1 u2 du R1 2 0 1 u2 du Re 2 1 u 1 u2 du Re 2 1 1 u2 du Re u 1 u2 du 1 Re 1 u2 du 1 Math 132 Final Exam Spring 2008 3 3 A thin triangular plate is submerged vertically in water so that one side is level with the water s surface The plate is a right triangle with two sides of length 1 Let w be the weight density of water Calculate the force of the water on the surface of the plate A w 6 B w 5 C w 4 D w 3 E w 2 F w G 2w 3 H 2w 5 I 2w 7 J 3w 5 Math 132 Final Exam Spring 2008 4 Calculate the Taylor polynomial T2 x at x 1 for f x ln x A x 1 x 1 2 6 B x x2 3 C x x2 2 D x x2 6 E x x2 2 F x 1 2 x 1 2 G x 1 x 1 2 H x 1 x 1 2 2 I x 2x2 J x 1 x 1 2 2 4 Math 132 Final Exam Spring 2008 5 5 Use the error bound formula to find an upper bound on the error f 1 5 T3 1 5 in approximating f 1 5 by its Taylor polynomial centered at x 1 Assume that f 4 u 2 for all u between 1 and 1 5 A 1 269 B 1 136 C 1 192 D 1 428 E 1 320 F 1 284 G 1 216 H 1 36 I 1 196 J 1 96 Math 132 Final Exam Spring 2008 6 6 Solve the initial value problem 2 yy 0 xe y A y p ln x2 B y cosh x2 2x 1 C y ln x2 e D y ln x2 e p E y ln x2 e 2 F y ex 2x C G y 12 ln x2 e H y 12 ln x2 e 2 I y e x C J y 12 ln x2 y 0 1 Math 132 Final Exam Spring 2008 7 7 A cup of coffee cooling off in a room at temperature 30 C has cooling constant k 0 08 min 1 If the coffee is served at a temperature of 90 C how long should you wait until its temperature drops to 60 C A 15 2 min B 20 3 min C 3 9 min D 10 2 min E 16 6 min F 8 7 min G 4 8 min H 5 1 min I 2 7 min J 12 5 min Math 132 Final Exam Spring 2008 8 Find the solution of the initial value problem y y 0 3y 1 y 0 2 4 A y 4 1 e 3t B y 4 1 e 3t C y 2 1 e 3t D y 2 1 e 3t E y 4 1 e 4t F y 2 1 2e 2t G y 3 1 4e 2t H y 2 1 4e 3t I y 2 1 4e 3t J y 4 1 e 2t 8 Math 132 Final Exam Spring 2008 9 9 Find the solution of the initial value problem y 0 3y e 3x A x 1 e 3x B 1 x e 3x C 2x 1 e 3x D xe 3x e3x E x 1 e 3x F e 3x e3x G e 3x e3x H e 3x xe3x I x 1 e3x J 1 x e3x y 0 1 Math 132 Final Exam Spring 2008 10 10 A 200 gal tank contains 100 gal of water with a salt concentration of 0 1 lb gal Water with a salt concentration of 0 4 lb gal flows into the tank at a rate of 20 gal min The fluid is mixed instantaneously and water in pumped out at the same rate it flows into the tank What is the limiting salt concentration for large t A 31 1 lb gal B 1 3 lb gal C 0 9 lb gal D 7 8 lb gal E 45 7 lb gal F 0 6 lb gal G 0 5 lb gal H 0 4 lb gal I 0 3 lb gal J 32 2 lb gal Math 132 Final Exam Spring 2008 11 11 Find the term a4 of the sequence defined recursively by the equations a0 0 a1 1 an an 1 an 2 for n 2 A 12 B 11 C 10 D 9 E 8 F 7 G 6 H 5 I 4 J 3 Math 132 Final Exam Spring 2008 12 12 Let the n th term of a sequence be defined by an n n 1 Find the smallest number M such that an 1 0 0001 for all n M A 2000 B 200 C 20 D 1000000 E 100000 F 10000 G 99999 H 9999 I 999 J 99 Math 132 Final Exam Spring 2008 13 Find the limit lim n A e B e2 C e 1 D e 2 E 0 F 1 G 2 H n I n J e2 n 1 13 2 n n Math 132 Final Exam Spring 2008 14 Consider the two series X 1 1 a ln n ln n 1 n 2 14 b X n n 1 1 Do these series converge If they do what is their value A a converges to 1 ln 2 b converges to 1 B a converges to 1 ln 2 b diverges C a converges to 0 b diverges D a diverges b converges to 1 E a diverges b diverges F a converges to 1 ln 2 b converges to 0 G a converges to 1 2 b diverges H a converges to 1 2 b converges to I a diverges b converges to 2 J a diverges b converges to 5 2 Math 132 Final Exam Spring 2008 15 Find the value of the series X n 3 A e 3 1 e 2 B e e2 1 C e 2 1 e 3 D e e3 2 E e 1 1 e 3 F e3 e2 1 G 1 1 e 2 H 1 …
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