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- 2. Let g(x)= {-1/5x + 2, x<0 -2, x=0 x+2, x>0. Does the lim g(x) x→0 exist? If yes, give its value. If not, why?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. 0Let 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
- Given 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 0.08True or False? b). If f(4) = 9, then it must be true that lim(x->4) f(x)= 0 If the statement is TRUE, explain why. If the statement is FALSE, sketch the graph of a counterexample.3. Evaluate lim x→5 √x+4-3/ x-5. Show your complete solution. 4. Evaluate lim x→1 x-1/ √x-1. Show your complete solution. 5. Prove that lim t→-2 √1-t3/t +3/2 / t+2= 1/4. Show your complete solution.
- Calculate lim(x->-2) (x^2- 2x -8)/(x^2 -x -12). Show all work.At x=-2, the graph has a:¯Removable discontinuity (hole)¯Jump discontinuity¯Vertical asymptote¯Horizontal asymptote¯None of the above12-Determine the equation of any asymptote and coordinate of holes forF(x)= -12x^3 +44x^2 -32x -16 / (3x^2 +7x+2) Please note that dont use the Lim's formulaLet (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.
- 5. Given the graph of g(x) = {√−x−2+1, x<-2 x2+2x+5, x≥-2 below, evaluate its limit as x approaches -2. a. 3 b. 1 c. the limit does not exist d. 5 6. Evaluate lim g(x) x→-3-. a. 18 b. - ∞ c.0 d. ∞ 7. Let g(x) = -1/x2. Evaluate lim g(x) x→0 by drawing its graph. a. ∞ b. 1 c. 0 d. -∞1. What are horizontal and vertical asymptotes? Give examples.Calculate lim(x-> 4) (x^2 -2x -8)/(x^2 -x -12). Show all work.At x = 4, the graph has a:¯Removable discontinuity (hole)¯Jump discontinuity¯Vertical asymptote¯Horizontal asymptote¯None of the above