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Question

limx1logxx1 is equal to

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Solution

We have, limx1logxx1

At x=0, the value of the expression is the form 00

Applying L'Hospital Rule, we get
limx1ddxlogxddx(x1)

limx11x1=limx11x

Since, (ddxlogx=1x)

Putting x=1, we get the value of the limit as 11=1


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