Calc please help

Limit as x approaches zero (1/x-1/tanx)

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asked by Sarah
  1. massage the form to

    1/x - cosx/sinx
    = (cosx-x)/(x*sinx)

    and apply l'Hospital's Rule

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    posted by Steve
  2. That is where I am confused ...

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    posted by Sarah
  3. Oops. A typo. Should be
    (x*cosx-sinx)/(x*sinx)

    just take derivatives, top and bottom. The limit is the same as for

    (-x*sinx+cosx-cosx)/(sinx + xcosx)
    = (-x sinx)/(sinx + x cosx)

    still -> 0/0, so do it again:

    (-sinx - x*cosx)/(cosx + cosx - x*sinx)
    -> 0/2 = 0

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    posted by Steve

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