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# If $f(5)=15,f'(5)=3$ then $\lim\limits_{x\to 5}\large\frac{xf(5)-5f'(x)}{x-5}$ is

$(a)\;15\qquad(b)\;0\qquad(c)\;3\qquad(d)\;None\;of\;these$

$\lim\limits_{x\to 5}\large\frac{xf(5)-5f(x)}{x-5}\qquad\big[\large\frac{0}{0}\big]$form
$\Rightarrow \lim\limits_{x \to 5}\large\frac{f(5)-5f'(x)}{1}$
$\Rightarrow \large\frac{15-5\times 3}{1}$
$\Rightarrow 0$
Hence (b) is the correct answer.