Further to my previous post Very simple limits question to clarify my understanding , here's a related question. Let $f(x)=\sqrt x,x\geq 0$. What is the limit of $f$ as $x$ tends to $0$?
I think the answer is $0$, but my textbook claims that the limit doesn't exist because $f$ is not defined on any punctured neighbourhood of $0$, ie. $f$ doesn't have a left-sided limit. But since f is undefined on the negative reals, would you say that $f$'s limit at $0$ is $0$ (and not require a left limit in this case), or would you say that $f$'s limit at $0$ is non-existent (because it has no left-sided limit)?
ps. It's at Example 2c if you type in page 184 in the box on http://www.scribd.com/doc/74564079/Mathematical-Analysis.