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Question

The value oflimx031+sinx31sinxxis


A

2/3

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B

-2/3

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C

3/2

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D

-3/2

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Solution

The correct option is A

2/3


limx031+sinx31sinxx=limx0(1+sinx)(1sin s)(1+sin x)2/3+(1+sin x)2/3+(1sin x)2/3(1sinx)2/3×1x=limx02(1+sin x)2/3+(1+sin x)1/3+(1sin x)1/3+(1sinx)2/3×sin(x)x
= 23.1=23


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