Question

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

Answer 1

`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]}