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Question

Find the value of xlim1x1+x1x21

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Solution

We have,
limx1x1+x1x21

Putting the limits we find it to be in 00 form using L' Hospitals rule.
=limx112x1+12x2x2x21=limx112x1+12xxx21=limx1x212x1+x212xx=limx1x1x+12x1+x212xx=limx1x+12+x212xx

Putting the limits we get
=221=12

Hence, this is the answer.

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