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Question

limxalogx-alogex-ea=


A

0

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B

1

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C

a

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D

dose not exist

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Solution

The correct option is B

1


Explanation for the correct option:

Find the value of limxalogx-alogex-ea

The given equation is,

I=limxalogx-alogex-eaI=loga-alogea-eaI=log0log0I=--

Using the L' Hospitality rule

limxafxgx=limxaf'xg'x

I=limxa1x-a.11ex-ea.exI=limxaex-eaexx-aI=ea-eaeaa-aI=00form

Using the L' Hospitality rule

I=limxaex-0exx-a+ex1-0I=ea-0eaa-a+ea1I=ea0+eaI=1

Hence, the correct answer is option (B).


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