Mathematics - Limits Question with Solution | TestHub

$\begin{array}{rl}& \underset{x\to \frac{\pi }{2}}{\lim }\frac{0-\{\sin (2x)+\cos (x)\}\cdot 3x^2}{2\left(x-\frac{\pi }{2}\right)}\\ & =\underset{x\to \frac{\pi }{2}}{\lim }\frac{-\{2\sin x\cos x+\cos x\}3x^2}{2\left(x-\frac{\pi }{2}\right)}\\ & =\underset{x\to \frac{\pi }{2}}{\lim }\left\{\frac{2\sin x\sin \left(\frac{\pi }{2}-x\right)}{2\left(x-\frac{\pi }{2}\right)}+\frac{\sin \left(\frac{\pi }{2}-x\right)}{2\left(\frac{\pi }{2}-x\right)}\right\}3x^2\\ & =\left(1(1)+\frac{1}{2}\right)3{\left(\frac{\pi }{2}\right)}^2\\ & =\frac{9{\pi }^2}{8}\end{array}$