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Answer 1 · 2016-11-29T14:10:40

The asymptotes are in $x = pi/6+kpi/3; k in ZZ$

To simplify let's put:

$t=3x$

and first analyse $f(t)=tant/t$ .

The vertical asymptotes of $tan t$ are located in $t=pi/2+kpi$ for $k in ZZ$ .

if $t!=0$ this obviously does not change.

For $t=0$ we have:

$lim_(t->0) tan t/t = lim_(t->0) sint/t*1/cost=1$

As $t=3x$ , the vertical asymptotes of $f(x)=tan(3x)/(3x)$ are located in:

$x = pi/6+kpi/3; k in ZZ$

graph{tan(3x)/(3x) [-5, 5, -2.5, 2.5]}