Numerical Methods for Ordinary Differential Equations: Initial Value Problems

NOTE:

Clearly label all plots (title, x-label, y-label, and legend).

When using Python, use the plt.subplot command from Matplotlib when comparing 2 or more plots to make comparisons easier.

1. Consider the function f(x) = 3 tan(x). (a) Compute the first 4 non-zero terms in the Taylor series of f(x) about the point r = T/4. (b) Using the results from Part (a), make a single Python plot which contains all of the following: i. a graph of f (x) versus x for x E, : ii. a graph of p1 (x). iii. a graph of P2(x). iv. a graph of p3(x). v. a title, r-axis label, y-axis label, and a legend. 12 1. Consider the function f(x) = 3 tan(x). (a) Compute the first 4 non-zero terms in the Taylor series of f(x) about the point r = T/4. (b) Using the results from Part (a), make a single Python plot which contains all of the following: i. a graph of f (x) versus x for x E, : ii. a graph of p1 (x). iii. a graph of P2(x). iv. a graph of p3(x). v. a title, r-axis label, y-axis label, and a legend. 12