1 f0?) : 1+3;2 Compute 1 x) : 1+x2 f(0) -2x JHCI') : (1+x2)2 HO) (6332! rim) : ( 2+1)3 f"(0) H! _ 24x(x2 1 Hf f (a?) (x2+1)4 f (0) . 24! 5x4- 10x2+ 1! , f'i'Wm) : ( 2+1)5 f'""(0) (v) -240x(x2-3H3x2-1! m f (it) : (2+1)6 f (0) We see that for the odd terms f(2k+1)(0) = 0 and we also see that for the even derivatives fi2k)(0) = Hence the Taylor series for f centered at [J is given by 24