5. Assume lim f (x) = L, where L # 0, and assume lim g(x) = 0. Prove that lim = co. You will need the X-C X-C x-cg(x) definition of this type of limit from Homework #7, Problem 4.\f(a) The statement lim = 00 x-022 makes intuitive sense. Construct a rigorous definition for a limit statement of the form lim f (x) = 00 x-+c using ideas like N, o, and , and use it to prove the limit statement concerning 1/x2. (b) Construct a definition for the statement lim f(x) = L. x-+00 Show that lim - = 0. (c) What would the definition of lim f(x) = 00 look like? Give an example of such a limit