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Question

limxπ2(1tanx2)(1sinx)(1+tanx2)(π2x)3 is equal to

A
18
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B
0
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C
132
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D
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Solution

The correct option is C 132
Put x=π2h as xπ2,h0

Given, limit =limh01tan(π4+h2)(1cosh)1+tan(π4+h2)(2h)3

=limh0tan(h2)limh02sin2(h2)8h3

=limh014⎜ ⎜ ⎜tanh22×h2⎟ ⎟ ⎟×limh0⎜ ⎜ ⎜sinh2h2⎟ ⎟ ⎟2×14

=132.

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