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Question

Evaluate: limx0x0sin2tcostdtx3

A
1
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B
12
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C
13
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D
23
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Solution

The correct option is C 13
Evaluate limx0x0sin2tcostdtx300 form

If we put x=0, in numerator then 00sin2tcostdt=0
In denominator 03=0

Now, apply L'Hospital's rule,

limx0sin2xcosx(dxdn)3x2=limx0cosx3(sinxx)2

=13(1)2=13 option C Answer

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