What are the horizontal and vertical asymptotes of: #f(x)=xtan(x)#?

1 Answer
Apr 23, 2018

#x != {pi} /2 + kpi, k in ZZ#

Explanation:

#tan(x)# is undefined for #{pi} /2 + k pi# where #k in ZZ#

For example: #{pi} /2,{3pi} /2,{5pi} /2...#

Therefore there will be vertical asymptotes at every #{pi} /2 + kpi#

There are no horizontal asymptotes, however, as the range is #y in RR#

graph{xtan(x) [-5.55, 5.55, -2.775, 2.774]}