Mathematics - Limits Question with Solution | TestHub

Let $f(x)={\underset{\mathrm{n}\to \infty }{\lim }}_{}{\tan }^{-1}\left(4n^2\left(1-\cos \frac{x}{n}\right)\right)$ and $g(x)={\underset{\mathrm{n}\to \infty }{\lim }}_{}\frac{n^2}{2}\ell n\cos \left(\frac{2x}{n}\right)$.

Then ${\underset{\mathrm{x}\to 0}{\lim }}_{}\left(\frac{e^{-2g(x)}-e^{f(x)}}{x^6}\right)$ is equal to