Let f(x)=4 and f^′(x)=4 . Then Lim_x arrow 2 (x f(2)-2 f(x))/(x-2) is given by

Correct answer: (C) -4. We have, Lim_x arrow 2 (x f(2)-2 f(x))/(x-2) (0/0 )=Lim_x arrow 2 f(2)-2 f^′(x)=f(2)-2 f^′(2)=4-2 × 4=-4

Q97 / 225 · JEE Main 2002 · Mathematics

Let $f(x)=4$ and $f^{\prime}(x)=4$. Then $\operatorname{Lim}_{x \rightarrow 2} \frac{x f(2)-2 f(x)}{x-2}$ is given by

A
2
B
-2
Correct answer
C
-4
D
3

Solution

We have, $\operatorname{Lim}_{x \rightarrow 2} \frac{x f(2)-2 f(x)}{x-2}\left(\frac{0}{0}\right)=\operatorname{Lim}_{x \rightarrow 2} f(2)-2 f^{\prime}(x)=f(2)-2 f^{\prime}(2)=4-2 \times 4=-4$

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

Let $f(x)=4$ and $f^{\prime}(x)=4$. Then $\operatorname{Lim}_{x \rightarrow 2} \frac{x f(2)-2 f(x)}{x-2}$ is given by

Solution

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