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5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
If  $f(x) = \left\{ \begin{array}{l}\frac{5}{2} - x\,,\,{\rm{when\,\,}}\,x < 2\\\,\,\,1\,\,\,\,\,\,,\,{\rm{when \,\,}}x = 2\\x - \frac{3}{2},{\rm{when\,\,}}\,x > 2\end{array} \right.$, then
  • A
    $f(x)$ is continuous at $x = 2$
  • ✓
    $f(x)$ is discontinuous at $x = 2$
  • C
    $\mathop {\lim }\limits_{x \to 2} f(x) = 1$
  • D
    None of these
✓

Answer

Correct option: B.
$f(x)$ is discontinuous at $x = 2$
b
(b) $\mathop {\lim }\limits_{x \to 2 - } f(x) = \frac{1}{2}$ and

$\mathop {\lim }\limits_{x \to 2 + } f(x) = \frac{1}{2}$ and $f(2) = 1.$

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