There may be a confusion regarding the meaning of “limit undefined”. It is actually a matter of opinion. My notion of “limit undefined” is different from that of your textbook. In your textbook, the limit is said to be undefined if it fails to exist as a number. So for instance the limit \[\lim_{x\to 0}\frac{1}{x^2}=\infty\] is undefined according to textbook. In my case however I would still say that the limit exists as \(\infty\) since the left-hand limit and the right-hand limit coincide as \(\infty\). It wouldn’t matter whichever definition you follow as long as you are clear about it.