# Continuity and Asymptotes

1. Sep 19, 2007

### 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.

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

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.

2. Sep 19, 2007

### HallsofIvy

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

3. Sep 19, 2007

### Garen

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.