Find the value of k for which ƒ(x) = {sin2x/5x, when x ≠0;λ, when x = 0 is continuous at x=0

Question

Find the value of k for which \(f(x) = \begin{cases} \frac{sin2x}{5x} , & \quad \text{when} \,\text{x≠0;}\\ λ , & \quad \text{when}\, \text{x=0} \end{cases}\) is continuous at x = 0

Answer 1

Since, f(x) is continuous at x=0