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

1 Answer
Jan 31, 2017

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]}