What is the value of \(a\) for which \(f(x)=\left\{\begin{array}{l}\sin x \quad if \quad x \leq \frac{\pi}{2} \\ a x \quad if \quad x>\frac{\pi}{2}\end{array}\right.\) is continuous?
Since the function is continuous, hence \[\] L.H.L. = R.H.L. \[\] \(\lim _{h \rightarrow 0} \sin \left(\frac{\pi}{2}-h\right)=\lim _{h \rightarrow 0} a\left(\frac{\pi}{2}+h\right)\) \[\] \(1=a \cdot \frac{\pi}{2} \Rightarrow \mathrm{a}=\frac{2}{\pi}\) \[\] Choice (C)\[\]
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