Concept explainers
Using the Definition of Limits at Infinity The graph of
(a) Find
(b) Determine
(c) Determine M, where
(d) Determine N, where
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Calculus: Early Transcendental Functions
- Let ƒ(x) = (3^x - 1)/x. a. Make tables of values of ƒ at values of x that approach c = 0 from above and below. Does ƒ appear to have a limit as x --> 0? If so, what is it? If not, why not? b. Support your conclusions in part (a) by graphing ƒ near c = 0.arrow_forward4. Given f(x)= { 1, if x < 0 x-1, if x ≥ 0 , estimate lim f(x) x→0- a.1 b. 0 c. does not exist d. -1 5. Given f(x)= { 1/x, if x < 4 x2, if x ≥ 4 , estimate lim f(x) x→4+ a. 1/4 b. 2 c. does not exist d. 16arrow_forwardFind all asymptotes of g, where g(x) = (e^x-e^-x)/(2e^x+3e^-x)(use limits in your solution)arrow_forward
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- evaluate the limits using the limit laws A) lim (x^3 - 2x^2 +1) x is approaching -1 B) lim (t^2 - t)/(t+1) t is approaching 1 C) lim (1+cos(x))/(x^3 +2)arrow_forwardLet (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.arrow_forward2. 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?arrow_forward
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