MATLAB CODE:

MATLAB CODE:

1. Write a subprogram to carry out the Romberg algorithm for a function f defined on an arbitrary interval [a, b]. The user will specify the number of rows to be computed in the array and will want to see the entire array when it has been computed. Write a main program and test your Romberg subprogram on these three examples: sin x 1 cosx - e b. The routines for these integrals should be written to avoid serious loss of significance due to subtraction. Also, it is customary to define a function f at any questionable point xo by the equation f (xo) - lim,-xo f(x). If the limit exists, this method guarantees continuity of f at xo. For the third example, make a suitable change of variable, such as x = 1/t. Compute seven rows in the Romberg array. Print the array in each case with a format that enables the convergence to be observed. 1. Write a subprogram to carry out the Romberg algorithm for a function f defined on an arbitrary interval [a, b]. The user will specify the number of rows to be computed in the array and will want to see the entire array when it has been computed. Write a main program and test your Romberg subprogram on these three examples: sin x 1 cosx - e b. The routines for these integrals should be written to avoid serious loss of significance due to subtraction. Also, it is customary to define a function f at any questionable point xo by the equation f (xo) - lim,-xo f(x). If the limit exists, this method guarantees continuity of f at xo. For the third example, make a suitable change of variable, such as x = 1/t. Compute seven rows in the Romberg array. Print the array in each case with a format that enables the convergence to be observed