Test1Spr2011 - Name MAC 3473 Honors Calculus 1 Keesling...

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Name MAC 3473, Honors Calculus 1 Keesling Test 1 2/2/2011 Do all problems. Show your work and explain your answers. Each problem is 20 points. 1. Show that the following series converge. (a) 2 n 4 n = 1 ! " (b) n 6 n n = 1 ! " 2. Determine the radius of convergence and the interval of convergence for the following series. (a) ( x + 3) n n n = 1 ! " (b) x ! 1 3 " # $ % & ' n n = 0 ( )
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3. Determine the power series for the following functions. (a) sin( x ) = a n x n n = 1 ! " (b) arctan( x ) = a n x n n = 0 ! " 4. Determine the first eight coefficients a 0 , a 1 , , a
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Test1Spr2011 - Name MAC 3473 Honors Calculus 1 Keesling...

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