Find all asymptotes of h(x) = xarctan(1/x^2)

[wheat0809]

I have a problem that I think I know the answer to, but I can't really figure out how to mathematically show my answer. I think there is an vertical asymptote at x=0 and horizontal asymptotes at x = + or - 1

Find all asymptotes of the function:

h(x) = xarctan(1/x^2)

I know to take the limit as x goes to infinity, but I am stuck from there?

Please help me.

 

[pka]

Did you graph the function?

 

[wheat0809]

Asymptotes

How do you type arctan in the calculator? And according to this graph my answer is wrong, right? How do you mathematically prove where the asymptotes are?

 

[tkhunny]

Asymptotes are not in the Domain. This one is pretty obviosu that x = 0 is a problem. Just look at the arguement of the arctangent.

Arctangent appears in several ways:

atan(x)
tan^{-1}(x)
Possibly, there is an "Inverse" button to press before tan(x)
It may be in a function listing.