<p>The entire math department can’t come up with the correct solution to this BC Calc question.</p>
<p>Let f be the function given by f(x)= e^(-2x^2) (read as e raised to the negative 2 x squared)</p>
<p>(a) Find the first four nonzero terms and the general term of the power seriews for f(x) about x=0.</p>
<p>(b) Find the interval of convergence of the power seriews for f(x) about x = 0. Show the analysis that leads to your conclusion.</p>
<p>(c) Let g be the function given by the sum of the first four nonzero terms of the power seriews for f(x) about x=0. Show that l f(x) - g(x) l < 0.02 for -0.6 less than or equal to x less than or equal to 0.6.</p>
<p>i can probably answer your question next year when I take Calc BC.</p>
<p>is it urgent?</p>
<p>yeah it can be done. its actually a simple task…but its pretty tedious. like taking all the weeds off my farm, this is conceptually easy but lots of work.</p>
<p>a. i probably wouldnt do the power series. id construct the maclaurin series for e^(-2x^2) man i wish i had LaTeX here. then id use the series to construct the general term for the maclaurin series of that function.</p>
<p>b. id find the interval of convergence for that general series by using something. id suspect that the interval of covergence is probably pretty evident after constructing the general series.</p>
<p>c. at first looked like something that required error bound…but its just proving that on the given interval, the difference between the sum of the first 4 terms and the given function itself < .02</p>
<p>once again, im lazy right now cause i studied my ass off today for chemistry…someone else will do it. if they cant, go to AoPS</p>