Find k if the function given below is continuous at f(x) = (2 cos x - sin 2x)/(π - 2x)^3, for x ≠ π/2

Question

Find k if the function given below is continuous at  \(x=\frac{\pi}{2}\)

\(f(x) = \frac{2cos\,x - sin\,2x}{(\pi - 2x)^3},\) for \(x \neq \frac{\pi}{2}\)

f(x) = (2 cos x - sin 2x)/(π - 2x)³, for x ≠ π/2

= k, for \(x = \frac{\pi}{2}\)

Answer 1

f(x) = (2 cos x - sin 2x)/(π - 2x)³

Given, f is continuous at \(x = \frac{\pi}{2}\)