Question

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

• A. 35
• B. -35
• C. 28
• D. -28

Answer 1

Answer: (D)

-28

Answer 2

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