Consider the function f (x) = sin(x) on the interval [0, π]. Use python to build the Vandermonde system to find the interpolating polynomial PN (x) to f (x) using 5, 10, 15 and 20 equally spaced nodes on [0, π]. Once you have the interpolating polynomials then evaluate the infinity norm of the error between f (x) and PN (x) on a fine grid consisting of 1000 equally spaced points on [0, π]. Report these errors and comment on the results. Repeat the problem above using the Hermite interpolation
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