Q$2.$ a$)$ Use the ideas of Richardson's extrapolation and Romberg's method to evaluate the first derivative of $f=e^x$ at $x=0.$

To construct the first column of the Romberg's table, use the formula $\frac{e^{x+h}-e^x}{h}$ and $h={10}^{-1},$ and proceed by halving

$h.$ Write a code to construct the Romberg's table and provide its output. Create a table as large as necessary to calculate all $15$

decimal places of the integral correctly, if possible. If not, how low does the error get with this approach? Is subtractive

cancellation still a concern? Compare the results with that of the previous question.

b$)$ Repeat part $($a$)$ starting with the formula $\frac{e^{x+h}-e^{x-h}}{2h}$ and $h={10}^{-1}.$