limx→1 1+log⁡x−x1−2x+x2 equals

$lim_{x \to 1} \frac{1 + \log x - x}{1 - 2 x + x^{2}}$ equals

A
1
B
$- 1$
C
0
D
none of these

Solution:

We have,

$lim_{x \to 1} \frac{1 + \log x - x}{1 - 2 x + x^{2}}$

[By L' Hospital's Rule]

$= lim_{x \to 1} \frac{\frac{1}{x} - 1}{2 (x - 1)} = lim_{x \to 1} \frac{1 - x}{2 x (x - 1)} = - \frac{1}{2}$

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