The function in the problem is \(f(x)= (8/x^3)-(6/x)\)

We have to find any vertical asymptotes of the graph. Based on the function itself, and a graph, I can tell there is a vertical asymptote at x=0, and that each one sided limit of x=0 is respectively infinite and negative infinite.

But, I was told to find the vertical asymptote by using a limit, since that is how the AP Calc test wants the work done.

I might just be having a brain f**t right now, but how do I evaluate \(lim(x\rightarrow0^+)((8/x^3)-(6/x))\) or \(lim(x\rightarrow0^-)((8/x^3)-(6/x))\) without just substituting and getting the limit equals 0?

Also this is a no calculator question.

Thanks

Guest Mar 2, 2018

edited by
Guest
Mar 2, 2018

edited by Guest Mar 2, 2018

edited by Guest Mar 2, 2018