Evaluate the limit.
First, we use the definition of the exponential, and the continuity of to write,
Next, we rewrite the term inside the limit to get it into the form and apply L’Hopital’s rule,
But, this final limit is a quotient of continuous functions, and the denominator is not zero, so it is continuous. Therefore, the value of the limit at is equal to the value of the function. Since the numerator is 0 and the denominator is when , we find that the limit is 0. Therefore,