MCQ
$\lim_\limits{\text{x} \rightarrow \text{a}}\frac{\text{x}-\text{a}}{|\text{x}-\text{a}|}=$
- A0
- B1
- C-1
- Ddoes not exist
Solution:
Using,
$ \lim_\limits{\text{x} \rightarrow 0}|\text{x}|=-\text{x}$
$ \lim_\limits{\text{x} \rightarrow 0}|\text{x}|=+\text{x}$
we get $\lim_\limits{\text{x} \rightarrow \text{a}}-\frac{\text{x}-\text{a}}{-(\text{x}-\text{a})}=-1$
$\lim_\limits{\text{x} \rightarrow \text{a}}+\frac{\text{x}-\text{a}}{-(\text{x}-\text{a})}=-1$
Since, LHL is not equal to RHL, hence the limit does not exist.
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