LIMITS (using \( L^{\prime} \) Hospital's rule \( \mathrm{P} \) Let...

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LIMITS (using \( L^{\prime} \) Hospital's rule
\( \mathrm{P} \)
Let \( f(a)=g(a)=k \) and their \( n^{\text {th }} \) order derivatives \( f^{n} \)
W
\( (a), g^{n}(a) \) exist and are not equal for some \( n \in N \).
Further, if
\( \lim _{x \rightarrow a} \frac{f(a) g(x)-f(a)-g(a) f(x)+g(a)}{g(x)-f(x)}=4 \), then
the value of \( k \), is
(1) 0
(2) 4
(3) 2
(4) 1
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