Limits

Step 1: Identifying the limit form.
We need to evaluate the limit: At , both the numerator and the denominator approach 0. Hence, we have a indeterminate form, which suggests that we can apply L'Hopital's Rule.
Step 2: Applying L'Hopital's Rule.
L'Hopital's Rule states that if the limit is of the form , we can differentiate the numerator and denominator separately and then evaluate the limit. The derivative of the numerator is: The derivative of the denominator is: Now, applying L'Hopital's Rule: Step 3: Evaluating the new limit.
At , the numerator becomes , and the denominator becomes . Therefore, the limit simplifies to: Thus, the value of the limit is: