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Tough derivative definition

  1. Jun 2, 2014 #1

    joshmccraney

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    Gold Member

    hey pf!

    can you help me with this $$\lim_{h \to 0} \frac{f(x+3h^2) - f(x-h^2)}{2h^2}$$

    i know the definition and have tried several substitutions, but no help. anyone have any ideas?
     
  2. jcsd
  3. Jun 2, 2014 #2

    joshmccraney

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    Gold Member

    nevermind, lopitals rule did the trick
     
  4. Jun 2, 2014 #3

    lurflurf

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    Homework Helper

    hint 1
    $$0=\mathrm{f}(x)-\mathrm{f}(x)$$
    hint 2
    $$\lim_{h \to 0} \frac{f(x+3h^2) - f(x-h^2)}{2h^2}=\lim_{h \to 0}\left[\frac{3}{2}\frac{\mathrm{f}(x+3h^2)-\mathrm{f}(x)}{3h^2}+\frac{1}{2}\frac{\mathrm{f}(x-h^2)-\mathrm{f}(x)}{-h^2}\right]$$
     
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