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Question

limx0(cosecx)1logx=


A

0

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B

1

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C

1e

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D

None of these

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Solution

The correct option is C

1e


Explanation for correct option:

Calculating the value of the limit:

Given expression is limx0(cosecx)1logx

Simplifying the expression:

=limx0(cscx)1logx=limx0e1lnxln(cscx)[elnax=ax]=limx0e-cotx1x[L'hospitalrule]=elimx0-1tanx1x=e-limx0xtanx[limx0tanxx=1]

Applying the limits:

=e-1

Thus,

limx0(cosecx)1logx=e-1=1e

Therefore, the correct answer is option (C).


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