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Question

The value of limx0 tan xsin xsin3 x is

A
1
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B
\N
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C
12
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D
32
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Solution

The correct option is C 12
limx0 tan xsin xsin3 x= limx0 tan xsin xx3×x3sin3 x= limx0 tan xsin xx3 × 1= limx0 (x+x33+2x515....)(xx33!+x55!....)x3= limx0 (x33+2x515....)(x33!+x55!....)x3= limx0 x3(13+2x215....+13!x25!....)x3= limx0 (12+x28....)= 12

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