The value of the limit $L$ is:

$L = 0.02778$

Would you like a more detailed explanation or have any questions?

Here are 5 related questions to consider:

1. What is the concept of limits in calculus?
2. How does the behavior of a function near a specific point determine the limit?
3. What are the typical strategies for evaluating complex limits?
4. How can L'Hopital's Rule be applied when limits lead to indeterminate forms?
5. What is the significance of continuous functions when discussing limits?

Tip: Always check if the function is continuous at the point you're evaluating the limit for smoother calculations.