limx→0tanx-xx2tanx equals to

limx0tanx-xx2tanx equals to

  1. A

    1/3

  2. B

    2/3

  3. C

    1/2

  4. D

    1

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    Solution:

    limx0tanx-xx2tanx=limx0sinx-xcosxx2sinx00 form 

    =limx0cosx-cosx+xsinx2xsinx+x2cosx

                       (using L'Hôpital Rule) 

    =limx0sinx2sinx+xcosx=limx0(sinx)/x(2(sinx)/x)+cosx=13

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