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Continuity of arctan x / x at 0.

  1. Oct 19, 2011 #1
    1. The problem statement, all variables and given/known data
    f:R->R is defined as f(x) when x[itex]\neq 0[/itex], and 1 when x=0.

    Find f'(0).

    2. Relevant equations

    3. The attempt at a solution
    Since I can prove that f is continuous at x=0, does that allow me to take the the limit of f'(x) as x-> 0, which is 0? It is quite easy to see that the correct answer must be f'(0)=0, but do i break any rules if I first differentiate f(x) and then look at the limit as x-> 0?

  2. jcsd
  3. Oct 19, 2011 #2


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    Just use lim(h→0) (f(x+h)-f(x))/h
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