we consider the series (i)what is the radius of convergence of this series? (ii)Compute the series expansion of the derivative f'(x) of f(x) around x=0. What is the coefficient of x^8 of this series ? (iii)what is the radius of convergence of the series for f'(x)? (iv)Calculate the series expansion of a primitive integral f(x)dx of f(x) around x=0. what is the coefficient of x^16? (v)what is the radius of convergence of the series for integral f(x)dx?