Do the following problems 1. Let f denote a real valued function defined on some open interval around a R. Consider a line of slope m and equation...

Do the following problems 1. Let f denote a real valued function defined on some open interval around a R. Consider a line of slope m and equation L(x) = f (a) + m(x - a) for all x R. Suppose that this line if the best approximation to the function f at a in the sense that |E(x)| lim = 0, xa |x - a| where E(x) = f (x) - L(x) for all x in the interval in which f is defined. Prove that f is differentiable at a, and that f (a) = m. 2. Recall that a function F : U