Question

Question #78ac4

Answer 1

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

Explanation:

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]}