find the limit of sqrt(x-4) as x approaches 4

[hndalama]

I'd like to clarify whether this limit exists. My thoughts are that the limit doesn't exist because the left side of 4 (i.e. x<4) is undefined throughout, so the left sided limit doesn't exist. Because the left sided limit doesn't exist, the limit cannot exist. Is this correct?

 

[tkhunny]

So, you noticed that a one-sided limit exists, but not both sides. How dies this fit into the definition of a limit? \(\displaystyle \delta-\epsilon\)?