More of What Could Go Wrong with Newton's Method To explore a few more examples of what could go wrong when using Newton's Method, consider the unction gwe look at the graph below, or look at the equation, it is obvious that the only zero of this function is x = 0 . So we just use this example to illustrate some things that go could awry when trying to use Newton's Method. a) Use Newton's Method with an initial approximation of x。 . Explain what goes wrong. b) Use Newton's Method with an initial approximation ofx1.1. Explain what goes wrong. c) Use Newton's Method with an initial approximation of xo = 0.3 . This one will approach the correct value, but explain what is not ideal about this approximation.
More of What Could Go Wrong with Newton's Method To explore a few more examples of what could go wrong when using Newton's Method, consider the unction gwe look at the graph below, or look at the equation, it is obvious that the only zero of this function is x = 0 . So we just use this example to illustrate some things that go could awry when trying to use Newton's Method. a) Use Newton's Method with an initial approximation of x。 . Explain what goes wrong. b) Use Newton's Method with an initial approximation ofx1.1. Explain what goes wrong. c) Use Newton's Method with an initial approximation of xo = 0.3 . This one will approach the correct value, but explain what is not ideal about this approximation.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:More of What Could Go Wrong with Newton's Method
To explore a few more examples of what could go wrong when using Newton's Method, consider the
unction gwe look at the graph below, or look at the equation, it is obvious that the only
zero of this function is x = 0 . So we just use this example to illustrate some things that go could awry
when trying to use Newton's Method.
a) Use Newton's Method with an initial approximation of x。 . Explain what goes wrong.
b) Use Newton's Method with an initial approximation ofx1.1. Explain what goes wrong.
c) Use Newton's Method with an initial approximation of xo = 0.3 . This one will approach the correct
value, but explain what is not ideal about this approximation.
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