please use java application that uses Recursion

(CLO 1) Create an interactive Java Application that uses recursion to solve the following: a) Calculate the value of ex = 1 + (x / 1 !) + (H/ 2!) + (x3 / 3!) + x are supplied by the user. You must call 2 recursive methods (One for factorial and another one for power (do not use pow method available in java). + (xn / n!), where n and b) Implement a recursive method, called vowels, that returns the number of vowels in a string. e) Write a recursive method to implement Newton method to find the square root of a nonnegative real number whithin a given tolerance. If you do not know Newton method here is a short description: Suppose x is a nonnegative real number, a is the approximate square root of x, and epsilon is the tolerance. Start with a = x; if la*a-k-epsilon, then a is the square root of x within the tolerance; otherwise replace a by (a "atx)/(2*a) and repeat, where la*a-xi denotes the absolute value of a*a-x. a, x, epsilon are given by the user