Homework Homework Assignment #29 Read Section 4.8 Page 277, Exercises: 1 – 53(EOO), 59 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 277 Show that L’Hôpital’s Rule is applicable and use it to evaluate the limit. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 277 Show that L’Hôpital’s Rule is applicable and use it to evaluate the limit. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 277 Show that L’Hôpital’s Rule is applicable and to evaluate the limit. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 277 Show that L’Hôpital’s Rule is applicable and evaluate. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 277 Apply L’Hôpital’s Rule to evaluate the limit. In some cases, it may be necessary to apply more than once. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 277 Apply L’Hôpital’s Rule to evaluate the limit. In some cases, it may be necessary to apply more than once. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 277 Apply L’Hôpital’s Rule to evaluate the limit. In some cases, it may be necessary to apply more than once. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 277 Apply L’Hôpital’s Rule to evaluate the limit. In some cases, it may be necessary to apply more than once. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 277 Apply L’Hôpital’s Rule to evaluate the limit. In some cases, it may be necessary to apply more than once. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 277 Apply L’Hôpital’s Rule to evaluate the limit. In some cases, it may be necessary to apply more than once. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 277 Apply L’Hôpital’s Rule to evaluate the limit. In some cases, it may be necessary to apply more than once. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 277 Apply L’Hôpital’s Rule to evaluate the limit. In some cases, it may be necessary to apply more than once. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 277 Evaluate the limit, using L’Hôpital’s Rule, if necessary. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 277 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 277 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 277 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Jon Rogawski Calculus, ET First Edition Chapter 4: Applications of the Derivative Section 4.8: Newton’s Method Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Sometimes we cannot find the real zeroes of a function via algebra. In such a situation, Newton’s Method may converge to root with sufficient accuracy. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

As illustrated in Figure 2, Newton’s Method is an iterative process that, if we have chosen a good initial estimate, will yield the desired zero to sufficient accuracy. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Derivation of Newton’s Method Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 282 Use Newton’s Method with the given function and initial value xo to calculate x1, x2, and x3. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 282 Use Newton’s Method with the given function and initial value xo to calculate x1, x2, and x3. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

As illustrated in figure 4, Newton’s Method doesn’t always work. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

As shown in Table 1, Newton’s Method doesn’t always converge to the root closest to the initial estimate. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 282 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework Homework Assignment #30 Read Section 4.9 Page 282, Exercises: 1 – 13(Odd) Rogawski Calculus Copyright © 2008 W. H. Freeman and Company