How can I determine if this function is continuous at x=1? Is 2/0 a discontinuity or infinity for a function? 
For the question: Given the function $ (x^2+1)/(x-1) $, is the function continuous at x=1? 
When I took the right hand and left limits, I got infinity in both cases and f(1) would be 2/0 which I was informed equals infinity, yet there is a vertical asymptote at x=1, which is an obvious indicator of discontinuity. In this case, will the function be continuous?

For a function $f(x)$ to be continuous at some point $c$ of its domain, it has to satisfy the following three conditions:


*

*$f$ has to be defined at $c$

*$\lim\limits_{x \to c} f(x)$ has to exist

*the value of the limit must equal to $c$


In your case, the function $\frac{x^2+1}{x-1}$ is not defined at $x=1$, so the function is not continuous.
