A graph of y = f(x) is shown and a c-value is given. Use the graph to find the following, whenever they exist. (If an answer does not exist, enter DNE.) C = -2 y 10 -10 -5 5 10 -5 -10
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- Below is a graph of the function g(x). Use this graph to complete the problems given below. a) lim x->2 g(x) =? b) lim x->0 g(x) =? c) lim x->4- g(x) =? d) lim x->4+ g(x) =? Based on the answrs in c and d does lim x->4 g(x) exist?1. Evaluate lim (2x-5) given its graph below. x →2 a.0 b. -1 c. 2 d. 1 2. Given the graph of f(x) below, evaluate its limit as x approaches 3. a.2 b. 3 c. 1 d. 0Use the graph of the function h(x) given below to answer the questions that follow. (1) Evaluate h(−2) (a) Find lim x → −2- h(x) (b) Find lim x → -2+ h(x) (c) Use your answers from parts (b) and (c) to find lim x→-2 h(x).
- True or False? b). If lim x -> 5f(x) = DNE, then f (5) =DNE.If the statement is TRUE, explain why. If the statement is FALSE, sketch the graph of a counterexample.Sketch a graph of a function satisfying the following properties. 1) lim f(x)= -2 x--> 5 2) f'(5)=DNE(a) What is wrong with the following equation? x2 + x − 12 x − 3 = x + 4 (x − 3)(x + 4) ≠ x2 + x − 12 The left-hand side is not defined for x = 0, but the right-hand side is. The left-hand side is not defined for x = 3, but the right-hand side is.None of these — the equation is correct. (b) In view of part (a), explain why the equation lim x → 3 x2 + x − 12 x − 3 = lim x → 3 (x + 4) is correct. Since x2 + x − 12 x − 3 and x + 4 are both continuous, the equation follows. Since the equation holds for all x ≠ 3, it follows that both sides of the equation approach the same limit as x → 3. This equation follows from the fact that the equation in part (a) is correct.None of these — the equation is not correct.
- Let G(x) = (x + 6)/(x2 + 4x - 12). a. Make a table of the values of G at x = -5.9, -5.99, -5.999, and so on. Then estimate limx--> -6 G(x). What estimate do you arrive at if you evaluate G at x = -6.1, -6.01, -6.001, .....instead? b. Support your conclusions in part (a) by graphing G and using Zoom and Trace to estimate y-values on the graph as x --> -6Use the graph of the function h(x) given below to answer the questions that follow. (1) Evaluate h(2). 2 DNE 4 (a) Find lim x → 2- h(x) (b) Find lim x → 2+ h(x) (c) Use your answers from parts (b) and (c) to find lim x → 2 h(x)f'(x) = (x-1)(x-2)(x-3)(x-4) What can be said about lim(x->infinity) if anything?
- let g(x) = x2 + x − 12 / |x − 3| (a) Find the following limits. (If an answer does not exist, enter DNE.) (i) lim x → 3+ g(x) (ii) lim x → 3− g(x) (b) sketch the grapha)Find the domain of the function f and graph the domain of f. b) Show that lim (x,y) —>(0,1) f (x, y) cannot be found.1.What is the value of lim f(x) ? 2.What is the value of f(c)? 3.What would be the value of f(c) so that the function will be continuous at x=-3? 4.Does f(c) exist?