The value of limx→1 tan⁡πx4tan⁡πx2 is

The value of limx1tanπx4tanπx2 is

  1. A

    e-2

  2. B

    e-1

  3. C

    e

  4. D

    1

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    Solution:

    limx0tanπx4tanπx2

    =elimx1tanπx41tanπx2=elimx1sinπx4cosπx4cosπx42sinπx4cosπx4cosπx2

    =elimx12sin2πx42sinπx4cosπx4cosπx2 =elimx11cosπx2sinπx2cosπx2

    =elimx1sinπx2×π2cosπx2×π2sinπx2×π2 =e1

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