Given the domain in , is it possible to for to cause to be undefined for , where is a natural number? Given the domain restriction, it would seem that ONLY in would cause to be undefined. Divide by zero is trivially obvious and is not in question.
The solution key says that in will cause to be undefined for all .
is , which is greater than the limit of , and is , which is less than the limit of . Their solution would also exclude . Furthermore, the only value of that will keep within the domain restriction is . So, why do they bring " " into consideration at all?