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STD 12 - 5. continuity and differentiation — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 5. continuity and differentiation1 Mark
MCQ
If $f(x) = \left\{ \begin{array}{l}1 + x,\;{\rm{when\,\, }}x \le 2\\5 - x,\,{\rm{when \,\,}}\,x \le 3\end{array} \right.$, then
  • ✓
    $f(x)$ is continuous at $x = 2$
  • B
    $f(x)$ is discontinuous at $x=2$
  • C
    $f(x)$ is continuous at $x = 3$
  • D
    None of these
✓

Answer

Correct option: A.
$f(x)$ is continuous at $x = 2$
a
(a) $\mathop {\lim }\limits_{x \to 2 - } f(x) = 3,\,\mathop {\lim }\limits_{x \to 2 + } \,f(x) = 3$ and $f(2)=3 $.

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