_ x 2 |x - 2| x - 2 = - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to 2} \frac{{|x - 2|}}{{x - 2}} = $

A
$1$
B
$-1$
✓
Does not exist
D
None of these

✓

Answer

Correct option: C.

Does not exist

c
(c) $\mathop {\lim }\limits_{x \to 2 - } \,\,\frac{{|\,\,x - 2\,\,|}}{{x - 2}} = \mathop {\lim }\limits_{h \to 0} \,\frac{{|\,\,2 - h - 2\,\,|}}{{2 - h - 2}} = - 1$

and $\mathop {\lim }\limits_{x \to 2 + } \,\,\frac{{|\,\,x - 2\,\,|}}{{x - 2}} = \mathop {\lim }\limits_{h \to 0} \,\frac{{|\,\,2 + h - 2\,\,|}}{{2 + h - 2}} = 1$

Hence limit does not exist.

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