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  4. If f(5)=7 and f'(5)=7 then displaystyle lim x arrow 5 (x f(5)-5 f(x)/x-5) is given by

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Q. If $f(5)=7$ and $f^{'}(5)=7$ then $\displaystyle\lim _{x \rightarrow 5} \frac{x f(5)-5 f(x)}{x-5}$ is given by

WBJEEWBJEE 2010Limits and Derivatives

Solution:

$\displaystyle\lim _{x \rightarrow 5} \frac{x f(5)-5 f(x)}{x-5} $
$=\displaystyle\lim _{x \rightarrow 5} \frac{f(5)-5 f^{'}(x)}{1}$
$=f(5)-5 f^{'}(5) =7-5 \times 7 $
$ =7-5 \times 7 =-28$