For Python

Question 2: Interpolation and fitting Consider the following function F(x) = cos? (xx) exp(-10x%), on the interval x E -1, 1), evaluated at N + 1 evenly spaced points fi = F(x) for i (0.....N}, where 2.1 Plot, for N = 9. 1. The original function F(x). 2. A scatter plot of the (x ) points. 3. An interpolating polynomial fitting through the data. 4. A degree four least squares fitting polynomial, fitting the data in a least squares sense as described in the week 6 lecture and workshops. 5. A cubic spline through the data generated using scipy. interpolate. PchipInterpolator provided with SciPy. You should choose how to present the plots so that the data presentation is clear and easy to understand. Question 2: Interpolation and fitting Consider the following function F(x) = cos? (xx) exp(-10x%), on the interval x E -1, 1), evaluated at N + 1 evenly spaced points fi = F(x) for i (0.....N}, where 2.1 Plot, for N = 9. 1. The original function F(x). 2. A scatter plot of the (x ) points. 3. An interpolating polynomial fitting through the data. 4. A degree four least squares fitting polynomial, fitting the data in a least squares sense as described in the week 6 lecture and workshops. 5. A cubic spline through the data generated using scipy. interpolate. PchipInterpolator provided with SciPy. You should choose how to present the plots so that the data presentation is clear and easy to understand