Mathematics - Limits Question with Solution | TestHub

Let $\mathrm{f}(\mathrm{a})=\mathrm{g}(\mathrm{a})=\mathrm{k}$ and their $n$th derivatives ${\mathrm{f}}^{\mathrm{n}}(\mathrm{a}),{\mathrm{g}}^{\mathrm{n}}(\mathrm{a})$ exist and are not equal for some $\mathrm{n}$. Further if ${\lim }_{x\to a}\frac{f(a)g(x)-f(a)-g(a)f(x)+f(a)}{g(x)-f(x)}=4$ then the value of $k$ is