Given a function f such that f(3)= 1 and $\displaystyle f^{(n)}(3)=\frac{(-1)^n n!}{(2n+1)2^n}$

(a) write the first four nonzero terms and the general term of the Taylor series for f around x= 3

(b) find the radius of convergence of the Taylor series

(c) show that the third degree Taylor polynomial approximates f(4) within 0.01