Mathematics - Limits Question with Solution | TestHub

$L=\underset{x\to \frac{3\pi }{4}}{\lim }\frac{4{\sin }^{2}x\cos x-\cos x+\sin x}{\sin x+\cos x}$

$L=\underset{x\to \frac{3\pi }{4}}{\lim }\frac{2\sin x\left({\sin }^{2}x+{\cos }^{2}x+2\sin x\cos x-1\right)-\cos x+\sin x}{\sin x+\cos x}$

$L=\underset{x\to \frac{3\pi }{4}}{\lim }\frac{2\sin x\left[(\sin x+\cos x{)}^2-1\right]-\cos x+\sin x}{\sin x+\cos x}$

$L=\underset{x\to \frac{3\pi }{4}}{\lim }\frac{2\sin x(\sin x+\cos x{)}^2-2\sin x-\cos x+\sin x}{\sin x+\cos x}$

$L=\underset{x\to \frac{3\pi }{4}}{\lim }\frac{\left(\sin x+\cos x\right)\left\{2\sin x\left(\sin x+\cos x\right)-1\right\}}{\sin x+\cos x}$

$L=\underset{x\to \frac{3\pi }{4}}{\lim }2\sin x\left(\sin x+\cos x\right)-1=-1$