Working with binomial series Use properties of power series, substitution, and factoring of constants to find the first four nonzero terms of the Taylor series centered at 0 for the following functions. Use the Taylor .series (1 + 4x) ?2

Solution 41EStep 1:In this problem we need to find the first four nonzero terms of the taylor series centered at ‘0’ for the function by using the taylor series : Consider , By , using we get = 1 -2(4x)+3 = 1 -2(4x)+3 = 1 - 8x + 48Therefore , the first four nonzero terms of the taylor series centered at ‘0’ for the function are 1-8 x + 48 . That is , 1, -8x , 48 ,. First term = 1 Second term = -8x Third term = 48 Fourth term =