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Question

The value of limx x[tan1(x+2x+2)tan1(xx+2)]is


A

1

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B

-1

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C

1/2

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D

-1/2

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Solution

The correct option is C

1/2


=limx x[tan1(x+2x+2)tan1(xx+2)]is=limx x tan1(x+1x+2xx+21+x+1x+2xx+2)\\

=limx x1(x+22x2+5x+4)=limxtan1(x+22x2+5x+4)x+22x2+5x+4×x(x+2)2x2+5x+4=1×12=12


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