Question

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

Answer 1

Vertical : `uarr x = k/2pi darr, k = +-1, +-2, +-3, ...`

Explanation:

As `x to 0, y to 3/2`.

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

As x to `xto k/2pi, f to +-oo, k = +-1, +-2, +-3, ...`,

giving vertical asymptotes

`x= k/2pi, f to +-oo, k = +-1, +-2, +-3, ...`.

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