Solution

We want to evaluate the limit: \ As x→0, the numerator approaches e⁰ − 1 − 0 = 1 – 1 – 0 = 0, and the denominator approaches 0² = 0. So, we have an indeterminate form of type 0/0and we can use L'Hôpital's Rule. Applying L'Hôpital's Rule once: As x→0, the numerator approaches e⁰ −1 = 1 – 1 = 0, and the denominator approaches 2(0)=0. We still have an indeterminate form of type 0/0​, so we apply L'Hôpital's Rule again. Applying L'Hôpital's Rule a second time: