Is the limit of a function as you approach a point always the same if you approach from either side? Would that hold true for vertical asymptotes, or would the limit be infinity and negative infinity?

Question

agreene · Answer

left and right limits do not always approach the same point, and yes vertical asymptotes can cause one to go to infinity and the other to approach negative infinity.

anonymous · Answer

simplest example, 
$$f(x)=\frac{1}{x}$$ limit as x goes to zero from the left is minus infinity, from the right infinity