$$\begin{gathered} \mathit{Q}\mathbf{ }\mathbf{17}\mathbf{.}\mathbf{ }Let f\left(x\right)= \left\{\begin{array}{cc}\frac{1-{\sin }^{3}x}{3{\cos }^{2}x},& if x<\frac{\mathrm{\pi }}{2}\\ a,& if x=\frac{\mathrm{\pi }}{2}\\ \frac{b\left(1-\sin x\right)}{{\left(\mathrm{\pi }-2\mathrm{x}\right)}^2},& if x>\frac{\mathrm{\pi }}{2}\end{array}\right\}. If f\left(x\right) is continuous at z=\frac{\mathrm{\pi }}{2}, find a and b. \\ \left[\mathit{A}\mathit{n}\mathit{s}\mathbf{.}\mathbf{ }a=\frac{1}{2} and b=4\right] \end{gathered}$$