Functions Question 227
Question: $ \underset{x\to 1}{\mathop{\lim }},\frac{1+\log x-x}{1-2x+x^{2}}= $
[Karnataka CET 2000; Pb. CET 2001]
Options:
A) 1
B) ?1
C) 0
D) $ -\frac{1}{2} $
Show Answer
Answer:
Correct Answer: D
Solution:
Applying L-Hospital?s rule, $ \underset{x\to 1}{\mathop{lim}},\frac{1+\log x-x}{1-2x+x^{2}}=\underset{x\to 1}{\mathop{lim}},\frac{\frac{1}{x}-1}{-2+2x}=\underset{x\to 1}{\mathop{lim}},\frac{1-x}{2x(x-1)} $ Again applying L-Hospital?s rule, $ \underset{x\to 1}{\mathop{lim}},\frac{-1}{4x-2}=-\frac{1}{2} $ .
BETA
