I'm using Pyhton 3 in Jupyter notebook.

I need to solve this problem with Pyhton 3.

The Taylor Series

$$ f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(x_0) }{n!} (x - x_0)^n $$

Also, can you explain each code you write?

Problem 3 Write a function to approximate the function, f(x), using a Taylor series. The Taylor series for the function, f(x), evaluated at zo is given by the expression: f f(x) = AD CO) (0 8o)" f(x) = -(x - 2o)" (9) n! n=0 , however, we often truncate this infinite sum at n= N and write the Taylor series as an approximation f(a) = Px(x) = PO) (28 6)" f(1) Pn(x) = (x - x0)" (10) The function, f(x), can then be written as f(x) = Px(x) + Rn(x) (11) By including more terms in the series, i.e., higher values of N, the truncation error reduces and the Taylor series becomes a better approximation for the function at xo. Demonstrate this by plotting the function RN(x) for different values of N for the following functions: 1. f(x) = ell at zo = 0. 2. f(x) = at xo = 4