Consider the function (4)/(1-2^(1/x))

1. Estimate the right-hand limit, lim x->0+ f(x). Back up your answer by making an analytic argument about f(x) for values of x that are close to 0 but larger than 0.

2. Estimate the left-hand limit, lim x->0- f(x). Back up your estimate by making an analytic argument about f(x) for values of x that are close to 0 but smaller than 0.

3 answers

Looking at the graph at

http://www.wolframalpha.com/input/?i=%284%29%2F%281-2^%281%2Fx%29%29+

I'm sure you can justify your analysis.
Does it have an undefined limit.
correct. The limit from the right is not the same as the limit from the left.

But both limits are finite.