Continuity and Asymptotes

[Garen]

1. The problem statement, all variables and given/known data

Going over examples of continuity and asymptotes in class, we came across this function:

f(x) = 6sin(x) / (√X)

I know that the numerator is bounded between -1 and 1, and that the denominator increases to infinity. But, my question is...what would be the horizontal asymptote(s) if the equation had been:


f(x) = tan(x) / (√X)



3. The attempt at a solution

I tried finding the limit both graphically and numerically, and failed to come to any solid conclusion.

http://i186.photobucket.com/albums/x79/garenzy/GRAPH.jpg

Looking at the data table even at intervals in the hundreds of thousandths didn't help.

http://i11.tinypic.com/4lyic00.jpg

When I tried analytically I became lost. I know that if the numerator increases faster than the numerator then the horizontal asymptote dne. I also am aware that if the denominator increases faster than the numerator, then the asymptote is 0. But since a tangent function isn't bounded by any limits, like a sinusoid function, I'm not sure how to figure this out.

[HallsofIvy]

Do you have any reason to believe it HAS a horizontal asymptote? Unlike sin(x), tan(x) goes to infinity regularly.

[Garen]

Do you have any reason to believe it HAS a horizontal asymptote? Unlike sin(x), tan(x) goes to infinity regularly.

See, I thought at first that because it increases without bound that there would be no horizontal asymptote(s). But for some reason I felt that I missed something, and I am second guessing myself.