Answered: ion of n (n ranging between 1 and 80)…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Question

USING PYTHON NOT MATLAB

We can use the sum of the first n terms of the Taylor series of e x with a = 0 to estimate the value of the exponential function. Using a logarithmic y axis, plot the fractional error in the estimated e x (compared to numpy.exp(x)) as a function of n (n ranging between 1 and 80) for (a) x = 15 and (b) x = −15. [You can plot the two cases either as different curves on the same plot or in different plots, whichever is clearer.] Discuss the contributions of truncation and roundoff to the fractional error for the different values of x and n. Also discuss how you could reduce truncation and roundoff errors in order to estimate e x more accurately using the Taylor series.

Expert Solution

Step 1: Program approach

Import the necessary libraries (numpy and matplotlib.pyplot)
Define the function to calculate the nth term of the Taylor series for $e^{x}$ (where x is the input parameter and n is the term number) and to calculate the estimated value of $e^{x}$ using the first n terms of the Taylor series
Define the function to calculate the fractional error between the estimated value of $e^{x}$ and the actual value (computed using numpy.exp(x))
Set the values of x for which the error is to be calculated (x = 15 and x = -15 in this case)
For each value of x, loop through the values of n from 1 to 80 (inclusive), and calculate the corresponding fractional error using the functions defined above
Plot the fractional error as a function of n for each value of x, using a logarithmic y-axis
Display the resulting plots