Please help with the following:

Determine the accuracy of the following approximation, using Taylor's Theorem. There can be more than one correct answer depending on your value for M, but use a reasonably small M.

e = 1+1+1/2!+1/3!+1/4!+1/5!

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- Nov 6th 2012, 04:49 AMkimsanders82Need help with approximation using Taylor's Theorem
Please help with the following:

Determine the accuracy of the following approximation, using Taylor's Theorem. There can be more than one correct answer depending on your value for M, but use a reasonably small M.

e = 1+1+1/2!+1/3!+1/4!+1/5! - Nov 6th 2012, 06:49 AMHallsofIvyRe: Need help with approximation using Taylor's Theorem
Do you know what "Taylor's theorem" is?

- Nov 6th 2012, 06:59 AMkimsanders82Re: Need help with approximation using Taylor's Theorem
Yes, I need help applying it with the M value from the remainder estimation theorem.

- Nov 6th 2012, 08:08 AMhollywoodRe: Need help with approximation using Taylor's Theorem
Hi kimsanders82,

I think HallsofIvy is just trying to figure out where you're stuck, and the place to start with this problem is Taylor's theorem.

Here's what the first step looks like: You want to estimate the value of the function $\displaystyle e^x$. Taylor's theorem gives:

$\displaystyle e^x = 1+x+\frac{x^2}{2!}+\frac{x^3}{3!}$$\displaystyle +\frac{x^4}{4!}+\frac{x^5}{5!}+R(x)$

where R(x)=...

If you understand how to get from the general form of Taylor's theorem to this expression, you should be able to say what R(x) is. The M comes in when you try to estimate what R(x) is (when x=1, of course).

Hope this helps.

- Hollywood