The value of _ x 3^ + |x-3| x-3 equals: - Vidyadip

MCQ

The value of $ \lim\limits_{\text{x} \rightarrow 3^{+}} \dfrac{|\text{x}-3|}{\text{x}-3}$ equals:

✓
$1$
B
$-1$
C
$0$
D
Does not exist

✓

Answer

Correct option: A.

$1$

for $ \text{x}=30^+,$
$ \text{ x}-3 > 0$
Let $\text{L}=\displaystyle \lim_{\text{x}-3^+}\dfrac {|\text{x}-3|}{\text{x}-3}$
$=\displaystyle \lim_{\text{x}\rightarrow 3^+}$
$=\dfrac{(\text{x}-3)}{(\text{x}-3)}$
$=\lim\limits_{\text{x}\rightarrow 3^+}(1)$
$=1$

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