MACHINE PROBLEM 2: Due September 17, 2020

1. Given f(x) at i/n, i=0,1,...,n, find the Lagrange polynomial L_n(x) interpolating 
   f at the points {i/n | i=0,1,...,n}.

2. Write a program which computes L_n(x) (at least 512 values in [0,1]) for n=4,8,16 
   in the following two cases:

   (a) f(x)= sin(2*pi*x)
   (b) f(x)= |x-0.5|

3. Turn in a program listing and four pictures, two for each case, where the original 
   function f and the three Lagrange polynomials are drawn for x in the interval [0,1]. 
   On the first picture display the function f and the Lagrange polynomials L_4 and L_8. 
   On the second picture display f and L_16.