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!
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!
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