# Need help with approximation using Taylor's Theorem

• Nov 6th 2012, 04:49 AM
kimsanders82
Need help with approximation using Taylor's Theorem

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 AM
HallsofIvy
Re: Need help with approximation using Taylor's Theorem
Do you know what "Taylor's theorem" is?
• Nov 6th 2012, 06:59 AM
kimsanders82
Re: 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 AM
hollywood
Re: 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