Let f(x) have a power series representation t(x) and suppose that f(0)=1, f'(0)=1, f''(0)=2, and f'''(0)=6 a. with only the information above, to what degree of accuracy can we estimate f(1)? b. if in

Let f(x) have a power series representation t(x) and suppose that f(0)=1, f'(0)=1, f''(0)=2, and f'''(0)=6

a. with only the information above, to what degree of accuracy can we estimate f(1)?

b. if in addition we also know that t(x) converges on the interval [-2,2] and that |f4 (x)|<15 on that interval, then to what degree of accuracy can we estimate f(1)?