Functions Question 258
Question: Let $ f(x)=4 $ and $ f’(x)=4 $ , then $ \underset{x\to 2}{\mathop{\lim }}\frac{xf(2)-2f(x)}{x-2} $ equals
[AIEEE 2002]
Options:
A) 2
B) ? 2
C) ? 4
D) 3
Show Answer
Answer:
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 $ .
BETA
