Venn Diagrams

Step 1: Apply L'Hopital's Rule.
We observe that both the numerator and denominator approach 0 as , which results in an indeterminate form . Therefore, we apply L'Hopital's Rule: where and .
Step 2: Differentiate the numerator and denominator.
First, differentiate the numerator: Now, differentiate the denominator:
Step 3: Apply the limits.
Now, apply the limit as :
Step 4: Conclusion.
The value of the limit is: