If a limit does not exist, does that make the left and right limits unequal?

Question

I was asked to pick a function for when the limit of f(x) as x approaches c from the right and left are unequal. I used the square root of x-2. Since it is undefined for x<2 and the left-hand limit as x approaches 2 is not defined, does that make it unequal? I got the answer wrong when I said that, so an explanation would help. Thanks!

Answer 1

In your case, with root (x-2), there actually is a limit, and that is just 0, even though it's one sided, because you are backing right up to the end of the domain.

 

To better answer the question, choose something that has a disconnect limited to just one point, like the greatest integer function, or something with division by 0.