Q93 / 160 · WBJEE 2010 · Mathematics

If $\mathrm{f}(5)=7$ and $\mathrm{f}^{\prime}(5)=7$ then $\underset{x \rightarrow 5}{ } \frac{x f(5)-5 f(x)}{x-5}$ is given by

  • A
    35
  • B
    -35
  • C
    28
  • Correct answer
    D
    -28

Solution

Hints: $\operatorname{Lt}_{x \rightarrow 5} \frac{x f(5)-\operatorname{tf}(x)}{x-5}=\operatorname{Lt}_{x \rightarrow 5} \frac{f(5)-5 f^{\prime}(x)}{1}=f(5)-5 f^{\prime}(5)=7-5 \times 7=-28$

Hence, the correct answer is option: 'D'.

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