Question: Let \(f\left( x \right)=\sum\limits_{n=0}^{\infty }{\frac{{{x}^{n}}}{n!}}\)

(a) Find the interval of convergence of f.

(b) Show that \(f'\left( x \right)=f\left( x \right)\)

(c) Show that \(f\left( 0 \right)=1\)

(d) Identify the function f.