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The value of  is

  1. 1
  2. -1
  3. 0
  4. Does not exist

Answer (Detailed Solution Below)

Option 4 : Does not exist
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Detailed Solution

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Concept:

For a limit to exist, Left-hand limit and right-hand limit must be equal.

Calculations:

For a limit to exist Left-hand limit and right-hand limit must be equal.

|x| can have two values 

|x | = - x when x is negative 

|x| = x when x is positive.

 = 

​​ = 

Here, 

Hence, does not exist. 

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