If f(x)= l k x |x| , if x<0 3, if x 0 . is continuous at x=0, the… - Vidyadip

MCQ

If $f(x)=\left\{\begin{array}{l}\frac{k x}{|x|} \text {, if } x<0 \\ 3, \text { if } x \geq 0\end{array}\right.$ is continuous at $x=0$, then the value of $k$ is

✓
$-3$
B
$0$
C
$3$
D
any real number

✓

Answer

Correct option: A.

$-3$

$\text {} f(x)=\left\{\begin{array}{l}\frac{k x}{|x|}, \text { if } x<0 \\ 3, \text { if } x \geq 0\end{array}\right. $
Since, $ f $ is continuous at $ x=0,$
$\Rightarrow \quad \text { L.H.L }=\text { R.H.L. }=f(0) $
$\Rightarrow \quad \lim _{x \rightarrow 0^{-}} f(x)=\lim _{x \rightarrow 0^{+}} f(x)=f(0)$
$\Rightarrow \quad \lim _{x \rightarrow 0^{-}} \frac{-k x}{x}=\lim _{x \rightarrow 0^{+}} 3=3 $
$\Rightarrow k=-3 $

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