Question #78ac4

1 Answer
Nov 29, 2016

Answer:

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]}