2.13 Newton's Method

By the end of your studying, you should know:
Onscreen applet instructions:
Type a starting value followed by the Enter key. Try different starting values and observe the effect. Can you explain what happens when the starting value is 1?
ExamplesConsider the equationand say you intend to solve it using Newton's method. If the initial value chosen is not 0, what will happen when you apply Newton's method? Using Newton's Method, find the equation of the line of maximum slope tangent to the curve y = sin(x) that passes through the origin. Give the answer to 6 decimal places.
Use Newton's Method to approximate to 6 decimal places the solution to the equation
AppletsNewton's Method
VideosSee short videos of worked problems for this section.
QuizExercisesSee Exercises for 2.13 Newton's Method (PDF).Work online to solve the exercises for this section, or for any other section of the textbook. 
Resources on the WebInformation on NewtonBiographical data from St. Andrew's University's Web site Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"
Information on Leibniz
Calculus Applications
Newton's Method

Interesting ApplicationAlthough we are studying realvalued functions of a real variable, Newton's Method can be applied to complex numbers as well. The results yield some interesting pictures that show socalled Newton Basins, the set of iterative points leading to the solution. 
2.12 Derivatives of Exponential and Logarithm Functions  Table of Contents  2.14 Linear Approximations 
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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel