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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 $\lim _{x \rightarrow a} \frac{f(a) g(x)-f(a)-g(a) f(x)+f(a)}{g(x)-f(x)}=4$ then the value of $k$ is
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4
4
$\lim _{x \rightarrow a} \frac{k 9(x)-k f(x)}{9(k)-f(x)}=4$ (By L'Hospital rule)
$\lim _{x \rightarrow a} k \frac{9^{\prime}(x)-f^{\prime}(x)}{9^{\prime}(x)-f^{\prime}(x)}=4$ or $k=4$
$\lim _{x \rightarrow a} k \frac{9^{\prime}(x)-f^{\prime}(x)}{9^{\prime}(x)-f^{\prime}(x)}=4$ or $k=4$
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