A) 2
B) ? 2
C) ? 4
D) 3
Correct Answer: C
Solution :
\[y=\underset{x\to 2}{\mathop{\lim }}\,\frac{xf(2)-2f(x)}{x-2}\] Þ \[y=\underset{x\to 2}{\mathop{\lim }}\,\frac{xf(2)-2f(2)+2f(2)-2f(x)}{x-2}\] Þ \[y=\underset{x\to 2}{\mathop{\lim }}\,\frac{-2f(x)+2f(2)+xf(2)-2f(2)}{(x-2)}\] Þ \[y=\underset{x\to 2}{\mathop{\lim }}\,-2\frac{[f(x)-f(2)]}{x-2}+\underset{x\to 2}{\mathop{\lim }}\,\frac{f(2).(x-2)}{(x-2)}\] Þ \[y=-2\underset{x\to 2}{\mathop{\lim }}\,\frac{f(x)-f(2)}{x-2}+f(2)\] Þ \[y=-2\,\,\underset{x\to 2}{\mathop{\lim }}\,{f}'(x)+f(2)=-\,8+4=-\,4\].
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