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

$\lim_{x \to \infty} f (x)$

$\lim_{x \to - \infty} f (x)$

Accepted Answer

$\lim_{x \to \infty} f (x)$ $= \frac{1}{5}$

$\lim_{x \to - \infty} f (x)$ $= \frac{1}{5}$

Horizontal asymptote: $y=\frac15$

Answer

$\lim_{x \to \infty} f (x)$ $= \frac{1}{5}$

$\lim_{x \to - \infty} f (x)$ $= - \frac{1}{5}$

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

Answer

$\lim_{x \to \infty} f (x)$ $= \frac{1}{5}$

$\lim_{x \to - \infty} f (x)$ $= - \frac{1}{3}$

Horizontal asymptotes: $y equals 3$ and $y = - 3$

Answer

$\lim_{x \to \infty} f (x)$ $= \frac{1}{5}$

$\lim_{x \to - \infty} f (x)$ $= - \frac{1}{3}$

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