If f(x) = |x - 2|, then - Vidyadip

MCQ

If $f(x) = |x - 2|$, then

A
$\mathop {\lim }\limits_{x \to 2 + } f(x) \ne 0$
B
$\mathop {\lim }\limits_{x \to 2 - } f(x) \ne 0$
C
$\mathop {\lim }\limits_{x \to 2 + } f(x) \ne \mathop {\lim }\limits_{x \to 2 - } f(x)$
✓
$f(x)$is continuous at $x = 2$

✓

Answer

Correct option: D.

$f(x)$is continuous at $x = 2$

d
(d) Here $f(2) = 0$

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

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

Hence it is continuous at $x = 2$.

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