WBJEE · Maths · Limits
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
- D -28
Answer & Solution
Correct Answer
(D) -28
Step-by-step Solution
Detailed explanation
Hints: \(\operatorname{Lt}_{x \rightarrow 5} \frac{x f(5)-\operatorname{tf}(x)}{x-5}=\operatorname{Lt}_{x \rightarrow 5} \frac{f(5)-5 f^{\prime}(x)}{1}=f(5)-5 f^{\prime}(5)=7-5 \times 7=-28\)
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