Reproduce Figure 7.1 by performing the following

Chapter , Problem 1

(choose chapter or problem)

Reproduce Figure 7.1 by performing the following calculations: (a) Solve the initial-value problem dy/dt = 2t y2, y(0) = 1. (b) Given the interval 0 t 2 and n = 20, calculate the Euler approximation y20 to y(2). (Double-check your calculations by comparing your results to those given at the beginning of the section.) (c) Calculate the total error e20 involved in your approximation. (d) Repeat the calculations in parts (b) and (c) using n = 1000, 2000,..., 6000. (e) If your computer is up to the task, compute en for additional intermediate values of n. (Figure 7.1 was done with n ranging from 100 to 6000 by steps of 100.) (f) Some computer math systems can determine the best fit for this data to a function of the form K/n. If your computer can do this, determine the best value of K for this initial-value problem. Plot the data and the graph of K/n on the same axes.