Posted: September 13th, 2017

Calculus

Assignment Requirements

I need workings and solution to each part of the problem.

Question:

Suppose that is a solution of the equation. Show that:

           For arbitrary

And hence, show that,

         (1)

Furthermore, show that

And use (1) to arrive at

Conclude that if F then we have the error equation,

Assuming that there are positive constants and such that and for all near the root show that,

for some positive constant C. Discuss the following:

• What are the limitations of this result?
• Newton’s method is said to converge quadratically? Why?
• If has three digits of accuracy how many would you expect to have?
• How about? Explain your answers.

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