Cal 2 test 2 - Math 1592 - Calculus II Sample Test 2 1. Do...

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Unformatted text preview: Math 1592 - Calculus II Sample Test 2 1. Do the following converge (explain)? ln n n4 + 1 , n=1 1 n3 + 1 , n=1 n=1 1 1 + 2 n n , en , n! n=1 (2n)! , (n!)2 n=1 1 , ln(n + 1) n=1 1 n(n + 1) , n=1 n-1 n + 1, n=1 (2n)! (n!)2 , n=1 n=2 1 ln (n) 2 , 1 n ln n , n=3 n=1 2n 1 . +1 2. Determine whether the following series converge absolutely, conditionally or diverge (-1)n (n - 1) , n+1 n=1 (-1)n 2n + 3n , n=1 n=1 (-1)n n(n + 1) , (-1)n nn , n! n=1 (-1)n n n2 + 1 , n=1 (-1)n n n+1 , n=1 3. Calculate the nth degree Taylor polynomial with remainder for the following. Expand about the point c (i) f (x) = ex , c = 1, c = 0 n = 2 (iii) f (x) = ln(x + 1), c = 0, n=3 (ii) f (x) = sin x, c = (iv) f (x) = , 2 n=4 n = 3. 1 , c = 0, 2-x 4. Determine the interval of convergence of the following 2n x n n + 1, n=1 (-1)n x2n 22n (n!)2 , n=1 (2x - 1)n n2 , n=1 5. Given the following power series 1 = 1 + x + x2 + x3 + x4 1-x find a power series for the following (i) 1 , (1 - x)2 (ii) x tan-1 x (iii) 3 centered at x = 1. 4-x 1 ...
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This test prep was uploaded on 04/10/2008 for the course MATH 1592 taught by Professor Liu during the Spring '08 term at University of Central Arkansas.

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