MCQ
$\lim_\limits{\text{x} \rightarrow \text{a}}\frac{\text{x}-\text{a}}{|\text{x}-\text{a}|}=$
  • A
    0
  • B
    1
  • C
    -1
  • D
    does not exist

Answer

  1. does 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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