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Question

limx1(1x2)1log(1x)=

A
e
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B
1e
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C
1e2
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D
e2
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Solution

The correct option is A e
k=limx1(1x2)1log(1x)
Applying log on both the sides,
logk=limx11log(1x)log(1x2)
k=elimx1log(1x2)log(1x)
It is of the form 00, so applying L-Hospital's rule
k=elimx12x(1x2)11x
k=e

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