104s11noans

(f diverges because the terms do not approach 0 2 15

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Unformatted text preview: (f) diverges because the terms do not approach 0. 2 15. The series 1 1 3 / 2 + 1 2 3 / 2- 1 3 3 / 2 + 1 4 3 / 2 + 1 5 3 / 2- 1 6 3 / 2 + 1 7 3 / 2 + 1 8 3 / 2- 1 9 3 / 2 + · · · (a) converges because the terms approach 0. (b) diverges because the terms do not approach 0. (c) converges by the alternating series test. (d) diverges by the alternating series test. (e) converges by the absolute convergence test and p-test. (f) diverges by the absolute convergence test and p-test. 16. The series ∞ summationdisplay n =1 (- 1) n n 2 n − 1 x n is convergent precisely for the following values of x : (a)- 1 2 < x ≤ 1 2 (b) 0 ≤ x < 4 (c) x ∈ {- 2 , 2 } (d)- 2 < x ≤ 2 (e) x = π (f) x < 5 17. ∞ summationdisplay n =0 (ln 2) n n ! (a) = π . (b) = e . (c) = 2. (d) = 4 ln(2). (e) = cos(2). (f) diverges. 18. Find the coefficient of x 10 in the Maclaurin series expansion of f ( x ) = 4- x sin( x 3 ). (a) 0 (b) 4 (c) 10 (d) 1 / 6 (e) 1 / 10 (f) 1 / 10! 19. Suppose that y = f ( x ) satisfies the differential equation dy dx + y x + 1 = y , and also satisfies the intitial condition that y = 5 when x = 0. What is the value of y when x = 3? (a) e 3 (b) e − 1 (c) 4 e − 3 / 5 (d) 4 e 3 / 5 (e) 5 e − 3 / 4 (f) 5 e 3 / 4 20. A certain population grows according to the differential equation dP dt = P 20 ( 1- P 4000 ) and the initial condition P (0) = 1000. What is the size of the population at time t = 10? (a) 1751 (b) 1000 + 20 /e (c) 4000 e 1 / 20 (d) 1000 + 200 e 1 / 20 (e) 4000 / (1 + 3 e − 1 / 2 ) (f) 1000 / (1 + 20 e − 10 ) 3...
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(f diverges because the terms do not approach 0 2 15 The...

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