Chornys Quiz 2 Solutions

Chornys Quiz 2 Solutions

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Unformatted text preview: a − 1 − ln e −1 − 1 + ln e − 1 − ln b − 1 = a →1 b →1 The limit does not exist ? divergent. 1 ∞ e ∑ e 3 n =1 n−1 = D e e 1− 3 = 3e 3− e Let u = e x du = e x dx If x = −1 then u = e −1 If x = 1 then u = e C B 5. ∫ ∞ x 2 e − x dx 3 −∞ ∞ du 3 lim = ∫ e −u −∞ lim b − u 0 1 = e − u du + e du b → ∞ ∫0 3 a → −∞ ∫ a lim 1 lim −u 0 −u b = a → −∞ − e a + b → ∞ − e 0 3 lim lim − b 1 e −a − e + e0 = − e0 + 3 a → −∞ b→∞ 1 lim a e = 3a → ∞ =∞ ? Divergent [ 6. ∞ 2 ∑ n2 −1 n =2 ∞ =∑ n =2 ∞ [ 2 (n + 1)(n − 1) 3 Let u = x du = 3x 2 dx As x → ∞ , u → ∞ As x → −∞ , u → −∞ A(n − 1) + B(n + 1) = 2 A = −1 B A = ∑ + B =1 n +1 n =2 n − 1...
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This document was uploaded on 02/27/2014 for the course CALCULUS 81B at UWO.

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