1. Homework Homework Assignment #29 Read Section 4.8
Page 277, Exercises: 1 – 53(EOO), 59
Rogawski Calculus
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2. 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

3. 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

4. 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

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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

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

15. Homework, Page 277 Rogawski Calculus
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16. Homework, Page 277 Rogawski Calculus
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17. Homework, Page 277 Rogawski Calculus
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18. 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

19. 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

20. 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
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21. Rogawski Calculus
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22. Derivation of Newton’s Method
Rogawski Calculus
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23. Rogawski Calculus
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24. 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

25. 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

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

27. As shown in Table 1, Newton’s Method doesn’t always converge to
the root closest to the initial estimate.
Rogawski Calculus
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28. Example, Page 282 Rogawski Calculus
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29. Homework Homework Assignment #30 Read Section 4.9
Page 282, Exercises: 1 – 13(Odd)
Rogawski Calculus
Copyright © 2008 W. H. Freeman and Company