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 $f\left(x\right)=\frac{5x}{25x+3}$ :

$\lim_{x\rightarrow\infty}f\left(x\right)$

$\lim_{x\rightarrow-\infty}f\left(x\right)$

Accepted Answer

$\lim_{x\rightarrow\infty}f\left(x\right)$ $=\frac15$

$\lim_{x\rightarrow-\infty}f\left(x\right)$ $=\frac15$

Horizontal asymptote: $y=\frac15$

Answer

$\lim_{x\rightarrow\infty}f\left(x\right)$ $=\frac15$

$\lim_{x\rightarrow-\infty}f\left(x\right)$ $=-\frac15$

Horizontal asymptotes: $y=5$ and $y=-5$

Answer

$\lim_{x\rightarrow\infty}f\left(x\right)$ $=\frac15$

$\lim_{x\rightarrow-\infty}f\left(x\right)$ $=-\frac15$

Horizontal asymptotes: $y=5$ and $y=-5$

Answer

$\lim_{x\rightarrow\infty}f\left(x\right)$ $=\frac15$

$\lim_{x\rightarrow-\infty}f\left(x\right)$ $=-\frac15$

No horizontal asymptote

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}f(x)=25x+35x:limx→∞f(x)\lim_{x\rightarrow\infty}f\left(x\right)limx→∞f(x)limx→−∞f(x)\lim_{x\rightarrow-\infty}f\left(x\right)limx→−∞f(x)