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Here is a challenge

  1. Jan 10, 2010 #1
    My cousin challenges me with a tough limit problem.

    Compute the limit as x->0 of (sin(tanx)-tan(sinx))/(arcsin(arctanx)-arctan(arcsinx)).

    This limit seems impossible to do.

    I used L'Hopital's rule but it didn't help at all.

    Can anyone find a way to do it?
  2. jcsd
  3. Jan 10, 2010 #2
    Expand the numerator and the denominator as Taylor series up to the first significant term.
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