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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
If $f(x) = \left\{ \begin{array}{l}x + \lambda ,\;x\, < 3\\\,\,\,\,\,\,\,\,\,4,\,\,x = 3\\3x - 5,\,\,x > 3\end{array} \right.$ is continuous at $x = 3$, then $\lambda = $
  • A
    $4$
  • B
    $3$
  • C
    $2$
  • ✓
    $1$
✓

Answer

Correct option: D.
$1$
d
(d) By definition of continuity, we know that

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

$ \Rightarrow \,\mathop {\lim }\limits_{x \to 3 - } f(x) = 4$ or $\mathop {\lim }\limits_{h \to 0} 3 - h + \lambda = 4$ 

==> $3 + \lambda  = 4 ==> \lambda  = 1$

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