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Question

limx 0sin(x2)ln(cos(2x2x)) is equal to

A
2
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B
2
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C
1
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D
1
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Solution

The correct option is B 2
limx 0sin(x2)ln(cos(2x2x))
limx 0sin(x2)log(12sin2(2x2x2))
limx 0sin(x2)x2x2 log(12sin2(2x2x2))2 sin2(2x2x2)[2 sin2(2x2x2)]
=limx 0x22sin2(2x2x2)(2x2x2)21(2x2x2)2
=limx 02x2(2x2x)2=limx 02(2x1)2=2

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