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Question

Solve limx0sin1xtan1xx3 equal

A
1
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B
1
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C
1/2
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D
3/2
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Solution

The correct option is B 1/2
limx0sin1xtan1xx3

Applying L'Hopital here,limit becomes
limx011x211+x23x2

=limx0(1+x2)1x23x2(1+x2)1x2

Multiply numerator and denominator by (1+x2)+1x2 and we get
=limx0(1+x2)2(1x2)3x2((1+x2)+1x2)(1+x2)1x2

=limx03+x23((1+x2)+1x2)(1+x2)1x2

Putting in x=0 into the above equation, We get 12.

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