Question

$\underset{x\to 1}{lim}\frac{1+logx-x}{1-2x+x^2}$ equals

• A. $1$
• B. $-1$
• C. $0$
• D. None of the above

Answer 1

The correct option is D None of the above

We have,
$\underset{x\to 1}{lim}\frac{1+logx-x}{1-2x+x^2}$
$=\underset{x\to 1}{lim}\frac{\frac{1}{x}-1}{-2+2x}$ [By L' Hospital's Rule]
$=\underset{x\to 1}{lim}\frac{1-x}{2x(x-1)}=-\frac{1}{2}$
Hence, option 'D' is correct.