Find a power series representation for the function f ( x ) x ( 1 4 x ) 2 f ( x ) n 0 Determine the radius of convergence, R Use differentiation to find a power series representation for f ( x ) 1 ( 8 x ) 2 f ( x ) n 0 What is the radius of convergence, R R ( b ) Use part ( a ) to find a power series for f ( x ) 1 ( 8 x ) 3 f ( x ) n 0 What is the radius of convergence, R R ( c ) Use part ( b ) to find a power series for f ( x ) x 2 ( 8 x ) 3 f ( x ) n 2 What is the radius of convergence, R R

Question

Find a power series representation for the function  f ( x )   x ( 1   4 x ) 2 f ( x )   n   0 Determine the radius of convergence, R   Use differentiation to find a power series representation for f ( x )   1 ( 8   x ) 2   f ( x )   n   0 What is the radius of convergence, R   R   ( b ) Use part ( a ) to find a power series for f ( x )   1 ( 8   x ) 3   f ( x )   n   0 What is the radius of convergence, R   R   ( c ) Use part ( b ) to find a power series for f ( x )   x 2 ( 8   x ) 3   f ( x )   n   2 What is the radius of convergence, R   R

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Find a power series representation for the function. f ( x ) = x ( 1 + 4 x ) 2 f ( x )

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