Question

note: the language should be java on netbeans.

please solve the question complete.

Objective: The students will learn how to work with recursion and improve their problem solving skills.

Problem 1: Create an interactive Java Application that has a method to calculate the value of e x = 1 + (x / 1!) + (x2 / 2!) + (x3 / 3!) + … + (xn / n!) Where n and x are supplied by the user. Your must call 2 recursive methods (1 for factorial and another one for power (do not use pow method available in java).

Create an interactive Java Application that has a recursive method vowels that returns the number of vowels in a string.

Create an interactive Java Application that has a recursive method reverse that print a String in reverse.

Answer 1

public class Test {
        public static int fact(int n) {
                if(n <= 1) {
                        return 1;
                }
                return n * fact(n-1);
        }
        public static int power(int x, int n) {
                if(n == 0) {
                        return 1;
                }
                return x * power(x, n-1);
        }
        
        public static void main(String[] args) {
                
                Scanner in = new Scanner(System.in);
                
                int n, x;
                System.out.println("Enter value of x: ");
                x = in.nextInt();
                System.out.println("Enter value of n: ");
                n = in.nextInt();
                
                double value = 0;
                
                for(int i=0; i<=n; i++) {
                        int num = power(x, i);
                        int den = fact(i);
                        value += (num/(double)den);
                }
                
                System.out.println("Value of e^x is " + value);
                
                in.close();
        }
}

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