If f(x) = l , , , , x^2 , , when , ,x 1 + 5, when , , x > 1 ., th… - Vidyadip

MCQ

If $f(x) = \left\{ \begin{array}{l}\,\,\,\,{x^2},\,{\rm{when}}\,\,x \le 1\\x + 5,{\rm{when\,\, }}x > {\rm{1}}\end{array} \right.$, then

A
$f(x)$ is continuous at $x = 1$
✓
$f(x)$ is discontinuous at $x = 1$
C
$\mathop {\lim }\limits_{x \to 1} f(x) = 1$
D
None of these

✓

Answer

Correct option: B.

$f(x)$ is discontinuous at $x = 1$

b
(b) $\mathop {\lim }\limits_{x \to 1 - } f(x) = 1,\mathop {\lim }\limits_{x \to 1 + } f(x) = 6.$

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