Approximation of Functions

1. Write a MATLAB program to generate Chebyshev polynomials. (Hint: Use the M-file given in the book.)
2. Write a MATLAB program using Chebyshev polynomials to economize a Maclaurin series for $e^x$ in the interval [0,1] with a precision of $0.0001$. Tabulate the error values. (Hint: Utilize the M-file given in the book.)
3. The Chebyshev series and Maclaurin series for $e^x$ are given as the following;
   
   $$\begin{array}{l} e^x=0.9946+0.9973x+0.5430x^2+0.1772x^3 \\ e^x=1+x+0.5x^2+0.1667x^3\\ \end{array}$$
   
   
   • Tabulate the error values for the interval [-1,1].
   • Plot the error values for the interval.