If f(x) = * 20 c 2 5 - x , & when , , x < 3 5 - x, & when , , x >… - Vidyadip

MCQ

If $f(x) = \left\{ {\begin{array}{*{20}{c}}{\frac{2}{{5 - x}},}&{{\rm{when \,\,}}x < 3}\\{5 - x,}&{{\rm{when\,\, }}x > 3}\end{array}} \right.$, then

A
$\mathop {\lim }\limits_{x \to 3 + } f(x) = 0$
B
$\mathop {\lim }\limits_{x \to 3 - } f(x) = 0$
✓
$\mathop {\lim }\limits_{x \to 3 + } f(x) \ne \mathop {\lim }\limits_{x \to 3 - } f(x)$
D
None of these

✓

Answer

Correct option: C.

$\mathop {\lim }\limits_{x \to 3 + } f(x) \ne \mathop {\lim }\limits_{x \to 3 - } f(x)$

c
(c) $\mathop {\lim }\limits_{x \to 3 + } f(x) = 5 - 3 = 2,\,\mathop {\lim }\limits_{x \to 3 - } f(x) = \frac{2}{{5 - 3}} = 1.$

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