Assignment:

One way to calculate ex is to use the infinite series expansion

ex = 1 + x + x2/2! + x3/3! + x4/4! + ...

If the loop variable is named i, then the ith term is equal to xi/i!.

a. Write a method called myexp that adds up the first n terms of the series shown

above. You can use the factorial method from Section 5.10 or your iterative

version.

b. You can make this method much more efficient if you realize that in each iter-

ation the numerator of the term is the same as its predecessor multiplied by x

and the denominator is the same as its predecessor multiplied by i. Use this

observation to eliminate the use of Math.pow and factorial, and check that

you still get the same result.

c. Write a method called check that takes a single parameter, x, and that prints

the values of x, Math.exp(x) and myexp(x) for various values of x. The output

should look something like:

1.0 2.708333333333333 2.718281828459045

HINT: you can use the String "\t" to print a tab character between columns of

a table.

d. Vary the number of terms in the series (the second argument that check sends

to myexp) and see the effect on the accuracy of the result. Adjust this value

until the estimated value agrees with the “correct” answer when x is 1.

e. Write a loop in main that invokes check with the values 0.1, 1.0, 10.0, and 100.0.

How does the accuracy of the result vary as x varies? Compare the number of

digits of agreement rather than the difference between the actual and estimated

values.

f. Add a loop in main that checks myexp with the values -0.1, -1.0, -10.0, and

-100.0. Comment on the accuracy.

So far I have................

```
package myexp;
import java.util.Scanner;
public class Main {
public static void main(String args[]) {
double x, n, sum = 1 ;
int i;
Scanner read = new Scanner(System.in);
System.out.println("Enter the value of x: ");
x = read.nextDouble();
System.out.println("Enter the value of n: ");
n = read.nextDouble();
System.out.println ();
for(i = 1; i <= n; i++) {
sum += myexp(x,i);
}
System.out.println (sum);
}
public static double myexp( double x, int i) {
if (i == 1)
return x;
else
return Math.pow (x,i)/ factorial (i);
}
public static double factorial(double x, int n) {
double factorial = 1.0;
int i = 1;
while (i <= n) {
factorial = factorial * i;
i = i + 1;
}
return factorial;
}
}
```