List of top Mathematics Questions on Continuity asked in COMEDK UGET

If $$f(x) = \begin{cases} 2 \sin x & \text{for} \ -\pi \leq x \leq -\frac{\pi}{2}, a \sin x + b & \text{for} \ -\frac{\pi}{2}<x<\frac{\pi}{2}, \cos x & \text{for} \ \frac{\pi}{2} \leq x \leq \pi,\end{cases}$$and it is continuous on $[- \pi, \pi]$, then the values of $ a $ and $ b $ are:

If the derivative of the function \( f(x) = \begin{cases} b x^2 + ax + 4; & x \geq -1 \\ a x^2 + b; & x < -1 \end{cases} \) is everywhere continuous, then