# Math Help - In application of limits (Asymptotes)

1. ## In application of limits (Asymptotes)

Hi

In application of limits (Asymptotes)

$f(x)=x+1/x$ is the function

Hoxizontal Asymptotes

solution

$lim x-infinity f(x) = lim x-infinity [ x + 1/x ] = infinity$

but Vertical Asymptotes why? $limx-0$

$lim x-0 f(x) = lim x-0 [ x + 1/x ] = infinity$

thanks a lot

2. You should graph this function, you will see that it is supposed to have a vertical asymptote at y = 0 and a horizontal one at x = 1 . If you look at the infinite limit you can split it up using the common denominator:

$\frac{x + 1}{x} = 1 + \frac{1}{x}$

This is equivalent to the function you had before. Take the limits at infinity and zero of that and you will get a different answer for the horizontal asymptote.