_ x 3 x-3 |x-3| is equal to: - Vidyadip

MCQ

$\lim _{x \rightarrow 3} \frac{x-3}{|x-3|}$ is equal to:

A
1
B
-1
C
$0$
D
None of these

✓

Answer

(d) None of these
Explanation: $\lim _{x \rightarrow 3} \frac{x-3}{|x-3|}$
LHL at x = 3
$\lim _{x \rightarrow 3^{-}} \frac{x-3}{-(x-3)}[\because|x-3|=-(x-3) x<3]$
= -1
RHL at x = 3
$\lim _{x \rightarrow 3^{+}} \frac{x-3}{x-3}[\therefore|x-3|=x-3$, when $x>3]$
= 1
$LHL \neq RHL$

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