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Question

limx0sin(πcos2x)x2 is equal to.

A
π
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B
π
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C
π2
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D
1
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Solution

The correct option is A π
limx0sin(πcos2x)x2 (00form)
=limx0{cos(πcos2x)π2cosx(sinx)}2x
(using L'Hospital's rule)
=limx0πcos(πcos2x)cosx(sinxx)
=(π)(1)1(1)=π.

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