Please answer each question fully, providing all reasoning. You will be graded based on both mathematical correctness and clarity of writing. See the Written Portion Rubric on D2L for more details. 1. Let f be a function defined for all x, and continuous at all values of x except at 2 and 0. Suppose that i7 2 for all x > 10 we have that b S f (x) S :2 j; . Moreover, suppose that the following is known: lim f(x) : 3, lim f(x) :f(2) : 1, lim f(x) :f(0) : b, lim f(x) : 2. x%72' xsifr er' x904r (a) Does there always exist a value c on the interval ( 3, 0) such that f (C) = 0? Justify your answer. (b) Does there always exist a value c on the interval (1, 1) such that f (C) = 0? Justify your answer. (c) Evaluate the following limit: 13*)00 Justify your answer. Hint: In (a) and (b) 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 f ( x) is the information given in the prompt