The value of k, for which \(\mathrm{f}\left(\mathrm{x}\right)=\left{\begin{matrix}\frac{\sqrt{3}\mathrm{cosx}+\mathrm{si…

The value of k, for which \(\mathrm{f}\left(\mathrm{x}\right)=\left{\begin{matrix}\frac{\sqrt{3}\mathrm{cosx}+\mathrm{sinx}}{3\mathrm{x}+\frac{\pi }{2}}, & \mathrm{x}\neq -\frac{\pi }{3} \\ \mathrm{k}, & \mathrm{x}=-\frac{\pi }{3}\end{matrix}\right.\) is continuous at \(\mathrm{x}=-\frac{\pi }{3}\), is :