# How do you find the Vertical, Horizontal, and Oblique Asymptote given f(x) = (3x)/(Sin2x)?

Jan 31, 2017

Vertical : $\uparrow x = \frac{k}{2} \pi \downarrow , k = \pm 1 , \pm 2 , \pm 3 , \ldots$

#### Explanation:

As $x \to 0 , y \to \frac{3}{2}$.

The denominator is periodic. Yet, the ratio is non-periodic.

As x to $x \to \frac{k}{2} \pi , f \to \pm \infty , k = \pm 1 , \pm 2 , \pm 3 , \ldots$,

giving vertical asymptotes

$x = \frac{k}{2} \pi , f \to \pm \infty , k = \pm 1 , \pm 2 , \pm 3 , \ldots$.

graph{(3x)/sin (2x) [-50, 50, -25, 25]}