evaluate-the-following-limits-and-identify-the-horizontal-asymptotes-if-any-for-

Question

Evaluate the following limits and identify the horizontal asymptotes (if any) for the function f(x)=5x25x+3f\left(x\right)=\frac{5x}{25x+3}: lim⁡x→∞f(x)\$$lim_{x\rightarrow\infty}f$$\left(x\right)lim⁡x→−∞f(x)\$$lim_{x\rightarrow-\infty}f$$\left(x\right)

Accepted Answer

lim⁡x→∞f(x)\$$lim_{x\rightarrow\infty}f$$\left(x\right) =15=\frac15 ﻿lim⁡x→−∞f(x)\$$lim_{x\rightarrow-\infty}f$$\left(x\right) =15=\frac15 Horizontal asymptote: ﻿y=15y=\frac15y=51​﻿

Answer

lim⁡x→∞f(x)\$$lim_{x\rightarrow\infty}f$$\left(x\right) =15=\frac15 lim⁡x→−∞f(x)\$$lim_{x\rightarrow-\infty}f$$\left(x\right) =−15=-\frac15Horizontal asymptotes: y=5y=5 and y=−5y=-5

Answer

lim⁡x→∞f(x)\$$lim_{x\rightarrow\infty}f$$\left(x\right) =13=\frac13lim⁡x→−∞f(x)\$$lim_{x\rightarrow-\infty}f$$\left(x\right) =−13=-\frac13Horizontal asymptotes: y=3y=3 and y=−3y=-3

Answer

lim⁡x→∞f(x)\$$lim_{x\rightarrow\infty}f$$\left(x\right) =13=\frac13lim⁡x→−∞f(x)\$$lim_{x\rightarrow-\infty}f$$\left(x\right) =13=\frac13 No horizontal asymptote