Question 1. (11 points) Consider the graph of the function y = /(x) given below. For (a) (g), find each of the quantities. If a quantity does not exist or is undefined, explain why. (a) lim /() = (e) lim /(x) = (b) lim /(@) = (f ) lim /(z) = (c) lim /(x) = (g) lim/(@) = (d) /(-3) = (h) List the x-values where the function / is discontinuous. List for each discontinuity what kind of discontinuity it is (Removable, Jump, Infinite). Justify your answers. (i) List the x-values where the function f is not differentiable. Justify your answers.Question 2. (6 points) Evaluate the following limits. If the limit is infinite, specify the sign (too or -oo). If a particular limit does not exist, and is not infinite, explain why (a) Let a be a constant. Compute lim (b) Let c > 0 and a constant. Evaluate lim Let- veQuestion 3. (5 points) Prove that the polynomial p(x) = " + 2x7 - x + 1 has at least one real root. Question 4. (6 points) Consider the function defined as For which value(s) of c is / continuous everywhere?Question 5. (2+4 points) Consider the following piecewise defined function: if I -3 . Is / continuous at x = -2? Justify your answer. . Is / continuous at a - -37 Justify your answer.Question 6. (9 points) On the figure below, sketch the graph of a function f so that: (a) /(0) - 2 [f) lim /[!) - 4. (b) /(s) ,00 2:10, () for all s c | i, i), lim /(!) - /(s). (c) / is increasing on (0, 1). (h) f is discontinuous at I - 1. (d) lim /(t) - 60 (1) him /(g) -2 (e) / is defined everywhere. -2