Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 4: Applications of Derivatives - Section 4.6 - Newton's Method - Exercises 4.6 - Page 231: 8

Answer

Yes, see graph and explanations.

Work Step by Step

Step 1. Graph the function $y=cos(x)$ and label a few points as shown in the figure. Step 2. To estimate the solution of the function, we can use Newton's Method by approaching the zero with tangent lines. Step 3. Because the function has an infinite number of solutions, it is important to start within a short range of the zero to be estimated. In this case, to estimate $x=\frac{\pi}{2}$, the stating point should be $x_0\in(0,\pi)$ Step 4. If we start at $x_0=\frac{5\pi}{4}$, for example, we will end up getting the value of $x=\frac{3\pi}{2}$ as shown in the figure.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.