List of top Mathematics Questions on Continuity and differentiability asked in COMEDK UGET

If \[ y=\tan^{-1}\left( \frac{\sqrt{1+x^3}+\sqrt{1-x^3}} {\sqrt{1+x^3}-\sqrt{1-x^3}} \right) \] then \(\dfrac{dy}{dx}\) is equal to:

If \( 2y = \left[ \cot^{-1} \left( \frac{\sqrt{3} \cos x + \sin x}{\cos x - \sqrt{3} \sin x} \right) \right]^2 \ \quad \forall x \in \left( 0, \frac{\pi}{2} \right), \text{ then } \frac{dy}{dx} \text{ is equal to:}\)}

If \( f(x) = \begin{cases} \frac{1-x^m}{1-x}, & \text{for } x \neq 1 \\ 2m-1, & \text{for } x = 1 \end{cases} \) and the function is discontinuous at \( x = 1 \), then