Test1Spr2010

# Test1Spr2010 - (a sin x = a n x n n = 1"(b 1 1 x 2 = a...

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Name MAC 3473, Honors Calculus 1 Keesling Test 1 1/29/2010 Do all problems. Show your work and explain your answers. Each problem is 20 points. 1. Show that the following series converge. (a) 1 n 5 n = 1 ! " (b) n 3 3 n n = 1 ! " 2. Determine the radius of convergence and the interval of convergence for the following series. (a) ( x + 1) n n n = 0 ! " (b) x ! 1 2 " # \$ % ' n n = 0 ( )

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3. Determine the power series for the following functions.
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Unformatted text preview: (a) sin( x ) = a n x n n = 1 ! " (b) 1 1 + x 2 = a n x n n = ! " 4. Determine the first seven terms of the power series for the following functions. Explain how the terms are obtained. (a) 1 + x 7 = a n x n n = ! " (b) tan( x ) = a n x n n = ! " 5. Prove that the Geometric Series converges, x n n = ! " = 1 1 # x , for x < 1 ....
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Test1Spr2010 - (a sin x = a n x n n = 1"(b 1 1 x 2 = a...

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