If possible, redefine the function to make it continuous f(x) = (cos^2 x)/(1 - sin^3 x), for x < π/2

Question

If possible, redefine the function to make it continuous.

\(f(x) = \frac{cos^2 x}{1 - sin^3 x},\) for x < \(\frac{\pi}{2}\)

f(x) = (cos²x)/(1 - sin³ x), for x < π/2

\(=\frac{\sqrt{2}-\sqrt{1 + sin\,x}}{cos^2 x},\) for x > \(\frac{\pi}{2}\)

\(=\frac{2}{3},\) for x = \(\frac{\pi}{2};\) at  x = \(\frac{\pi}{2}.\)

Answer 1

f(x) = (cos²x)/(1 - sin³ x)

\(\therefore\) limit of the function does not exist

\(\therefore\) f has irremovable discontinuity a \(x = \frac{\pi}{2}\)