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Homework Help: Differentiability on a closed interval

  1. Jan 17, 2010 #1
    1. The problem statement, all variables and given/known data
    Hi all

    I wish to show differentiability of g(x)=x on the interval [-pi, pi]. This is what I have done:

    g'(a) = \mathop {\lim }\limits_{h \to 0} \frac{{g\left( {a + h} \right) - g\left( {a} \right)}}{h} \\
    = \mathop {\lim }\limits_{h \to 0} \frac{h}{h} \\
    = 1,

    for a in the interval [-pi,pi]. Hence we see that the derivative is 1 on this interval.

    Am I correct?

  2. jcsd
  3. Jan 17, 2010 #2


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    Sure, that's great.
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