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# (1 x 2 2 for x ≥ 0 f x = 0 for x ≤ for some

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Unformatted text preview: (1 + x 2 ) 2 for x ≥ 0; f ( x ) = 0 for x ≤ , for some constant A . Then the probability that the corresponding random variable lies between- 1 and 1 is: (a) 1 /e (b) 1 /π (c) 1 / 2 (d) 2 / 3 (e) π (f) 1 / √ 2 12. Determine the limit of the sequence x n = (- 3 . 14) n π n as n → ∞ . (a) 0 (b) ln 2 (c) 1 /π (d) √ 2- 1 (e) ln( π/ 2) (f) The limit does not exist. 13. The series 1- 1 2 2 + 1 3 2- 1 4 2 + 1 5 2- 1 6 2 + ··· (a) converges to a sum between 1 / 2 and 3 / 4. (b) converges to a sum between 3 / 4 and 1. (c) converges to a sum between 1 and 2. (d) converges to a sum that is greater than 2. (e) converges to a negative sum. (f) diverges. 14. The series ∞ summationdisplay n =2 2 n ln( n ) (a) converges by comparison with ∞ summationdisplay n =2 2 n . (b) diverges by comparison with ∞ summationdisplay n =2 2 n . (c) converges by the ratio test. (d) diverges by the ratio test. (e) converges by the integral test. (f) diverges by the integral test. 15. The series ∞ summationdisplay n =1 n ! e n (a) converges by the p-test. (b) diverges by the p-test. (c) converges because the terms approach zero....
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(1 x 2 2 for x ≥ 0 f x = 0 for x ≤ for some constant A...

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