_ x 1 1 |1 - x| = - Vidyadip

MCQ

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

A
$0$
B
$1$
C
$2$
✓
$\infty $

✓

Answer

Correct option: D.

$\infty $

d
(d) $\mathop {\lim }\limits_{x \to 1 - } \,\,\frac{1}{{|\,\,1 - x\,\,|}} = \mathop {\lim }\limits_{h \to 0} \,\,\frac{1}{{1 - (1 - h)}} = \infty $

and $\mathop {\lim }\limits_{x \to 1 + } \,\,\frac{1}{{|\,\,1 - x\,\,|}} = \mathop {\lim }\limits_{h \to 0} \frac{1}{{1 + h - 1}} = \infty $

Hence $\mathop {\lim }\limits_{x \to 1} \,\frac{1}{{|\,\,1 - x\,\,|}} = \infty .$

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