s09_mthsc208_hw16

# s09_mthsc208_hw16 - MTHSC 208(Dierential Equations Dr...

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MTHSC 208 (Differential Equations) Dr. Matthew Macauley HW 16 Due Monday March 23rd, 2009 (1) Use the ratio test to find the radius of convergence of the following power series: a. n =0 ( - 1) n x n , b. n =0 1 n + 1 ( x - π ) n , c. n =0 3 n + 1 ( x - 2) n , d. n =0 1 2 n ( x - π ) n , e. n =0 (5 x - 10) n , f. n =0 1 n ! (3 x - 6) n . (2) Use the comparison test to find an estimate for the radius of convergence of each of the following power series: a. n =0 1 (2 n )! x 2 n , b. n =0 ( - 1) n x 2 n , c. n =1 1 2 n ( x - 4) 2 n , d. n =0 1 2 2 n ( x - π ) 2 n . (3) Find the radius of convergence of the power series n =0 ( - 1) n 1 ( n !) 2 x 2 2 n . (4) The differential equation (1 - x 2 ) d 2 y dx 2 - x dy dx + p 2 y = 0 , where p is a constant, is known as Chebyshev’s equation. It can be rewritten in the form
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