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

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Answer 1 · 2018-04-23T15:10:30

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

$tan(x)$ 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]}

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