Continuity

To ensure that is continuous at , we need to satisfy the condition: We are given that , so we must find the limit of as . First, simplify the given function: We apply L'Hôpital's Rule because the limit leads to an indeterminate form .
Differentiating the numerator and denominator: Numerator: Denominator: Now, apply L'Hôpital's Rule: This shows that ensures continuity at , matching .
Conclusion.
Thus, the value of that ensures the function is continuous is 2, which corresponds to option (a).