Please code in Python, will leave a rating. Thank you.

2. (a) Implement the Barycentric Formula for evaluating the interpolating polynomial for arbi- trarily distributed nodes xo, ..., Xn; you need to write a function or script that computes the barycentric weights 1") = 1/IIk+j(x; xk) first and another code to use these values in the Barycentric Formula. Make sure to test your implementation. (b) Consider the following table of data X; f(x;) 0.00 0.0000 0.25 0.7071 0.50 1.0000 0.75 0.7071 1.25 -0.7071 1.50 -1.0000 Use your code in (a) to find P5(2) as an approximation of f(2). 2. (a) Implement the Barycentric Formula for evaluating the interpolating polynomial for arbi- trarily distributed nodes xo, ..., Xn; you need to write a function or script that computes the barycentric weights 1") = 1/IIk+j(x; xk) first and another code to use these values in the Barycentric Formula. Make sure to test your implementation. (b) Consider the following table of data X; f(x;) 0.00 0.0000 0.25 0.7071 0.50 1.0000 0.75 0.7071 1.25 -0.7071 1.50 -1.0000 Use your code in (a) to find P5(2) as an approximation of f(2)