We talked about the approximationf(x)f(c) +f(c)(xc)for values ofxclose toc. A more precise way to say this is thatf(x) =f(c) +f(c)(xc) +E(x),whereE(x) is an 'error' function measuring the difference betweenf(x) andthe linear approximation (you do not need to prove any of this). Note thatlimxcE(x) = 0.(a) By rearranging and taking an appropriate limit, show thatlimxc(E(x)xc)= 0.(b) Qualitatively, what does (a) say about the relative speeds with whichE(x)and (xc) approach 0 asxapproachesc? Why does this tell us that ourapproximation is a good one?