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Question

The value of limt0⎜ ⎜1t2t22tsintdt⎟ ⎟ equals to

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Solution

Let L=limt0⎜ ⎜1t2t22tsintdt⎟ ⎟ (00) form
Applying L'hospital rule, we get
L=limt0sint22tsin2t22t
L=limt0(sint2+2sin2t2t)
L=0+2=2

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