Limit And Continuity

To determine the value of 'a' that makes the function continuous at , we need to check the limit of as approaches 0 and ensure it equals .

First, find .

Using the well-known limit , let , then as , as well.

Thus, .

Therefore, .

To ensure continuity at , we require:

.

This yields .

Given the options, the correct value of 'a' that aligns with the provided options is .