If f(x) = l x + , ;x , < 3 , , , , , , , , ,4, , ,x = 3 3x - 5, ,… - Vidyadip

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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