Originally Posted by

**bcahmel** Suppose you used the first three nonzero terms of the power series representation to approximate $\displaystyle e^{-(x^2)}$ for $\displaystyle 0\le x \le 1/2$.

Obtain an upper bound on the error.

All the terms, are negative, I think? The parentheses confused me. So: power series representation is $\displaystyle 1-x^2-x^4/2-x^6/6...$

The approximation is found, I think, just by plugging in x=1/2, for which I got 0.71875.

Then use the Taylor Inequality...$\displaystyle R_3_(x) \le \frac{M}{(n+1)!} /x-a/^{n+1}$

$\displaystyle {f^{4}(x) \le M$

$\displaystyle \frac {(1/2)^6}{6} \le M$, so do I set M=1/384?

I stopped here because I wasn't sure if my value for M was right...I have the feeling it's not. Any help would be great.