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# B 2 c d 23 e f 1 ans d 15 solve the differential

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b) ! /2 c) ! d) 2/3 e) # f) 1 Ans: d 15. Solve the differential equation. x y y 5 7 = ! a. C y x = ! 2 2 5 7 b. C y x = + 2 2 7 5 c. C y x = ! 2 2 7 5 d. C y x = + 2 2 5 7 e. 5 x 2 + 7 y 2 = 12 Ans: c 16. Find the average value of f ( x ) = sin 2 x cos 3 x over the interval [– ! , ! ] a) ! b) 0 c) 5 d) 6 e) 12 f) 1 2 Ans: b 17. Consider the sequence defined by a n = ( ! 1) n + n ( ! 1) n ! n . Does this sequence converge and, if it does, to what limit? a) yes, to –1 b) yes, to 0 c) yes, to 1 d) yes, to 2 e) yes to ! f) diverges Ans a 18. Find the area of the surface obtained by rotating the curve y = 1 4 x 2 1 2 ln x , 1 ! x ! 2 about the y -axis. a. 2 101 b. 99 2 c. 48 d. 24 e. 12 f) none of these

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Ans: f
19. Use the Alternating Series Estimation Theorem or Taylor's Inequality to estimate the largest range of values of x for which the given approximation is accurate to within the stated error. 2 4 cos 1 , | | 0.08 2 24 x x x error ! " + < a) only for x = 0 b) –1 \$ x \$ 1 c) 7.2 6 ! x ! 7.2 6 d) –2 \$ x \$ 2 e) 57.6 6 ! x ! 57.6 6 f) – ! \$ x \$ ! Ans. e 20. Find a series representation for e x x dx ! . a) x n ( n + 1)! n = 0 ! " + C b) + C c) ln x + x n n i n ! + C n = 1 ! " d) ln x + n + 1 n ! x n + C n = 1 ! " e) (–1) n n x n + C n = 1 ! " f) ln x + 1 ( n + 1)! x n + 1 + C n = 1 ! " Ans: c
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b 2 c d 23 e f 1 Ans d 15 Solve the differential equation x...

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