# How do I find the asymptotes of #y=x/sin(x^2)#? Are there even any asymptotes?

##### 1 Answer

Feb 16, 2017

Vertical asymptotes :

See Socratic graph, for highlights.

#### Explanation:

The second factor has an indeterminate form

As

Besides this vertical asymptote x = 0, the others are given by the

zeros

Socratic asymptotes-inclusive graph, for

graph{(y-x/sin(x^2))=0 [-20, 20, -10, 10]}

4

graph{(x+.004y)(x-1.77+.005y)(x+1.77+.005y)(y-x/sin(x^2))(x-2.54-.003y)(x+2.54+.003y)=0 [-3.1416 3.1416 -10, 10]}

Ad hoc scales used to highlight asymptotes relative graph, for