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

$\mathop {\lim }\limits_{x \to a} {{f(a)g(x) - f(a) - g(a)f(x) + f(a)} \over {g(x) - f(x)}} = 4$

then the value of k is