1. Let f be a function defined for all x, and continuous at all values of I except at 2 and [1. Suppose that bxz + x for all x t:- lii we have that b s: x} -{ 12 _ b . Moreover, suppose that the following is known: lirn x} _ F5, lirn f[1}_ f[2] _ 1, lim x) _ f{i1J_ fi,. lirn x) _ 2. IrZ IiE'l' IP' Ir+ (a) Does there always exist a value c. on the interval (3, ll) such that ffc) _ U? Justify your answer. {b} Does there always exist a value c on the interval (1.1) such that e} U? Justify your answer. (c) Evaluate the following limit: lirn x). IH' Justify your answer. I lint: In {a} and {lo} we want to know if there always exists such a value c. Finding a specific example where such a c exists does not show that something always happens. The only thing you are allowed to assume about x) is the information given in the prompt