_ x 1 x x - 1 = - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to 1} \frac{{\log x}}{{x - 1}} = $

✓
$1$
B
$-1$
C
$0$
D
$\infty $

✓

Answer

Correct option: A.

$1$

a
(a) $\mathop {\lim }\limits_{x \to 1} \,\,\frac{{\log \,[(x - 1) + 1]}}{{x - 1}} = 1.$

Aliter : Apply $L-$ Hospital’s rule,

$\mathop {\lim }\limits_{x \to 1} \frac{{\log x}}{{x - 1}} = \mathop {\lim }\limits_{x \to 1} \frac{{\frac{1}{x}}}{1} = 1$

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