# Let f (x) be a given function that can be evaluated at points x0 ± jh, j = 0,1,2,…, for any fixed.

Let f (x) be
a given function that can be evaluated at points x0 ± jh, j = 0,1,2,…, for
any fixed value of h, 0 < h="">

(a) Find a
second order formula (i.e., truncation error O(h2)) approximating the third
derivative f (x0). Give the formula, as well as an expression for the
truncation error, i.e., not just its order.

(b) Use your
formula to find approximations to for the function f (x) = ex employing values
h = 10_1,10_2,…,10_9, with the default MATLAB arithmetic.
Verify that for the larger values of h your formula is indeed second order accurate.
Which value of h gives the
»

Let f (x) be
a given function that can be evaluated at points x0 ± jh, j = 0,1,2,…, for
any fixed value of h, 0 < h="">

(a) Find a
second order formula (i.e., truncation error O(h2)) approximating the third
derivative f (x0). Give the formula, as well as an expression for the
truncation error, i.e., not just its order.

(b) Use your
formula to find approximations to for the function f (x) = ex employing values
h = 10_1,10_2,…,10_9, with the default MATLAB arithmetic.
Verify that for the larger values of h your formula is indeed second order accurate.
Which value of h gives the closest approximation to e0 = 1?

(c) For the
formula that you derived in (a), how does the round off error behave as a
function of h, as h _ 0?

(d) How
would you go about obtaining a fourth order formula for f (x0) in general? (You
dont have to actually derive it: just describe in one or two sentences.) How
many points would this formula require?

»

## 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.