# 1. Suppose F e C4 in a interval containing the root, a and that Newton’s method…

1. Suppose F e C4 in a interval containing the root, a and that Newton’s method gives a sequence of iterates Ik, k = 0, 1, 2, … which converge to a. Show that Newton’s method is at least quadratically convergent to a if f'(a) # 0. If f'(a) = 0, then by using l’Hôpital’s Rule or otherwise, show that Newton’s method is linearly convergent in both of the cases (i)f”(a) 0 (ii)f”(a) = 0, f”(a) + 0. What is |Xk+1 – a lim k+ |3k – al in each of these cases? What can you say about the order of convergence of Newton’s method when f'(a) + 0, f”(a) = 0?

## Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
\$26
The price is based on these factors:
Number of pages
Urgency
Basic features
• Free title page and bibliography
• Unlimited revisions
• Plagiarism-free guarantee
• Money-back guarantee
On-demand options
• Writer’s samples
• Part-by-part delivery
• Overnight delivery
• Copies of used sources
Paper format
• 275 words per page
• 12 pt Arial/Times New Roman
• Double line spacing
• Any citation style (APA, MLA, Chicago/Turabian, Harvard)

# Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

### Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

### Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

### Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.