Answer (Detailed Solution Below)

Option 3 :
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Detailed Solution

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Calculation:

We have to find the value of 

       [Form ]

This limit is of the form , Here, We can cancel a factor going to zero out of the numerator and denominator.

Factor (√x  - 1) becomes zero at x tends to 1, So we need to cancel this factor from numerator and denominator.

Shortcut Trick

Let,

y = 

This is a 0/0 form. So we can apply L’Hopital’s rule.

Differentiating numerator and denominator separately,

We know that,

d(uv) = u dv + v du and 

⇒ y = 

⇒ y = 

⇒ y = 

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