In this example, since you need the limit near zero, the interval you should take is a neighborhood of zero as you said in the last sentence. But what are the allowable neighborhood of zero for this function? These are only the intervals of the form

with

. If you ignore this restriction, then

can take the value 1.5 (for example...anything larger than 1) and in this case you will get the interval

on which the function is not defined (since it is not defined on 1 or -1). The whole idea is to cover all neighborhoods of zero on which f is safely defined.