Problem: Find the domain and limits at endpoints of its intervals for the function

Solution: Since exponential accepts any argument, there are two conditions that determine the domain: The square root requires that x ≥ 0, the fraction requires (x − 1) ≠ 0. Thus the domain is

D( f ) = [0,1) ∪ (1,∞).

Therefore there are four limits to evaluate (when there is a point-sized hole in the domain, ti is usually better to do two one-sided limits there, although sometimes it turns out that a limit (both-sided) could have been done right away). We take it from the left, for tips on limit evaluation see e.g. Limits in Functions - Methods Survey.

Note that it was important to notice that 2 − e is a negative number, otherwise we get a wrong answer. Similarly we work with the limit at 1 from the right.

By the way, the results we learned suggest that the function goes like this.

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