6. (7 marks) (a) Let f be defined on [3, 45] with f(3) = 50 and f(45) = 2. If f is continuous on the interval (3, 45), is it true that there must be some number c E (3, 45) such that f(c) = 10? If you believe it is true, justify your reasoning. If you believe it is false, show it with an example. (b) Let g be some function such that g(2) = 1 and lim )2) - 6. Find the value of lim g(x). Please h -0 h justify all your reasoning. 1 2