Consider the function , f ( x ) x 7 ( 1 4 x ) 2 ( a ) Find the power series representation centered at x 0 Complete the given equation by entering an expression involving n and x Express your answer in such a way that the index n 0 gives the first non zero term of the power series Answer f ( x ) n 0 ( b ) Enter the first 5 nonzero terms of the power series ( These are expressions involving x , compatible with the indices n 0 , 1 , 2 , 3 , 4 in part ( a ) ) Answer f ( x ) E 4 ( c ) Find the radius of convergence for the power series about x 0 Answer

Question

Consider the function , f ( x )   x 7 ( 1 4 x ) 2   ( a ) Find the power series representation centered at x   0   Complete the given equation by entering an expression involving n and x   Express your answer in such a way that the index n   0 gives the first non   zero term of the power series  Answer  f ( x )   n   0 ( b ) Enter the first 5 nonzero terms of the power series  ( These are expressions involving x , compatible with the indices n   0 , 1 , 2 , 3 , 4 in part ( a )   ) Answer  f ( x )     E 4 ( c ) Find the radius of convergence for the power series about x   0   Answer

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Consider the function , f ( x ) = x 7 ( 1 4 x ) 2 . ( a ) Find the power series

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