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

Question

$(a)\;0\qquad(b)\;4\qquad(c)\;2\qquad(d)\;1$