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\f1. Evaluate the following limits or show they do not exist. Show all work. r' + 2r -8 (a) lim - Show work here: Final Answer:(e) At x = 0, f(x) (A) is continuous. (A) is continuous. (B) is discontinuous, since lim f() DNE. 3-+-3 (B) is discontinuous, since lim f(x) DNE. 2-+0 (C) is discontinuous, since f(-3) is unde- (C) is discontinuous, since f (0) is undefined. fined. (D) is discontinuous, since lim f(x) / f(0). (D) is discontinuous, since lim f(@) / 3-1-3 f (-3). Answer: (f) At = = -3, f(x) Answer: (g) True/False f is differentiable at o = 7. Answer:2. Consider the function f(x) graphed below. -10 -8 -2 10 -2 -4 -H -10 (a) lim f(x) (c) lim f(x) I-+2+ (b) lim f(x) (d) lim f(x) I-+2 7+-53. Take the derivative of the following functions (do not simplify). (a) f(x) = 13+8x+ Show work here: Final Answer: (b) f(x) =" - 3 +2: C- 8 Show work here:4. Find the equation of the tangent line to the curve y = (vr + 2) . (37 + 1) at the point s = 0. Show work here:(d) f() (x) = (e) Spot a pattern to find f() (x) =1 5. For f(x) = - find the following (hint: it might be useful to rewrite f(x) = x-?). (a) f(o)= (b) f" (x) = _ (c) f"(x) =(c) Compute the marginal profit when r = 20. Explain what this number means (specifically, think about what happens with the sale of the 21st bowl of cereal). Marginal profit at r = 20: Explanation:6. You and your roommate have a foodtruck selling cold cereals called: Frutier Loops @ (lawsuit for copyright infringement pending). After some analysis you find that the revenue function is R(x) = 120r, and the total cost is O(r) = 27-20x -500, where a = number of bowls of cereal sold. (a) Find the profit function. Final Answer: (b) Find the marginal profit function. Final Answer:7. The total profit you get from selling a cars is given by P(x) = -=2 + 30x + 4000. (a) Find the marginal profit function. Final Answer: (b) When is it profit maximized? Explain why this is a maximum and not a minimum. ( You might use a sign line to aid in your explanation, but your explanation should be a complete and grammatically correct sentence, think what would you say to your boss or an investor.)\f8. Consider the function 5 To+3r'+8 (a) Find the critical points of f- Final Answer: (b) Find the intervals where f is increasing and where it is decreasing. Final