# Limit question

How can you tell if a limit does not exit or that it goes to infinity?

example

lim$\underbrace{x\rightarrow}_{0}$($\frac{\sqrt{x+1}}{x}$)

The x goes to 0

The book says the limit is $\infty$ but if you take the left side limit you get -$\infty$ and if you take the right side of the limit you $\infty$. So wouldnt this limit not exist, because you have two different limits?