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- 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. 0Given lim (4x-3) as x approaches 1. Use the definition of a limt to find a number delta such that the absolute value of x-a is less than delta when the absolute value of f(x)-L is less than 0.08Let 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 --> -6
- . f (x) = x^2 +2 x<3 10 x=3 -3+4x x>3 1. At what value is this function discontinuous, if any? What is the lim f (x) 3 ? What is the lim f (x) 1? d. What is the value of f (4) ?Find the limit of the function (if it exists). (If an answer does not exist, enter DNE.) lim x→−4 x2-16/x+4 Write a simpler function that agrees with the given function at all but one point. Use a graphing utility to confirm your result. g(x) =the graph of the function f (x)=0.5x^2 satisfies lim x=1 f(x)=0.5
- Let (x) = |x - 2| / x - 2 A) what is the domain of g(x)? B) Use numerical methods to find lim x—> 2- g(x) and lim x—> 2+ g(x). C) based on your answer to (b), what is lim x—> 2 g(x)? D) sketch an accurate graph of g(x) on the interval [-4,4]. Be sure to include any needed open or closed circles.f'(x) = (x-1)(x-2)(x-3)(x-4) What can be said about lim(x->infinity) if anything?a)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.
- The graph of the function f is shown above. Which of the following statements is true? A) f is discontinuous at x = 0 because limx→0 f(x) does not exist. B) f is discontinuous at x = 3 because limx→3 f(x) ≠ f(3) C) f is discontinuous at x = 5 because limx→(5−) f(x) does not exist. D) f is discontinuous at x = 6 because limx→(6−) f′(x) ≠ limx→(6+) f′(x) Thank youThe graph of a function f for which f(2) exists and lim f(x) x-->2 exists, but the two are not equal. Construct an example of thisthe graph of f(x) is shown f(x)=(x^(2)+2x-3)/(x^(2)+4x-5) what is the limt of \lim_(x->\infty )f(x)? A; -5 B, 0 C, 1 D, \infty