Mathematics - Limits Question with Solution | TestHub

${\mathrm{Lt}}_{x\to 0}\frac{2\sin \left(\frac{x+\sin x}{2}\right)}{\frac{\sin x+x}{2}}\left(\frac{\sin x+x}{2}\right).{\mathrm{Lt}}_{x\to 0}\frac{2\sin \left(\frac{x-\sin x}{2}\right)}{\frac{x-\sin x}{2}}.\underset{x\to 0}{\mathrm{Lt}}\frac{1}{2}(x-\sin x)$ $\underset{x\to 0}{\mathrm{Lt}}\left(\frac{\sin x+x}{2x^4}\right)\cdot \frac{1}{2}\left[x-\left(x-\frac{x^3}{13}+\frac{x^5}{15}+\dots .\infty \right)\right]$