Continuity Of A Function

Step 1: Condition for continuity
For a function to be continuous at , we must have: That is:

Step 2: Factorizing denominator
We factorize as: Since the denominator becomes zero at , the numerator must also be zero at to avoid discontinuity.

Step 3: Finding
Substituting in the numerator:

Step 4: Computing limit
Now, we find: Factorizing the numerator: Canceling from numerator and denominator: Substituting : Thus, .

Step 5: Computing

Step 6: Conclusion
Thus, the final answer is: