# For what values of x, if any, does #f(x) = 1/((12x+4)sin(pi+(6pi)/x) # have vertical asymptotes?

##### 1 Answer

Vertical asymptotes :

Horizontal asymptote :

#### Explanation:

The asymptotes are given by

The horizontal asymptote is revealed by

The horizontal space between consecutive vertical asymptotes

diminishes from

asymptotes

You can study the second graph, for shape near the exclusive

asymptote

I have used ad hoc ( for the purpose ) scales, for clarity.

graph{(4y(3x+1)sin(6pi/x)+1)(x-6-.01y)(x+6+.01y)=0 [-16, 16, -.5, .5]}

graph{(4y(3x+1)sin(6pi/x)+1)(x+.333-.00001y)=0 [-.4 -.0,-10, 10]}