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Analytic functions

  1. Sep 9, 2008 #1
    1. The problem statement, all variables and given/known data

    Supposed f(z(0))=g(z(0))=0 and that f'(z(0)) and g'(z(0)) exist where g'(z(0)) is not equal to 0. Use definition (10, section 19 of derivative to show that :

    lim z->z(0) (f(z)/g(z))=f'(z(0))/g'(z(0))


    2. Relevant equations

    definition 1: f'(z(0))=lim z->z(0) f(z)-f(z(0))/(z-z(0)

    3. The attempt at a solution

    f'(z(0))= lim (z->z(0)) f(z)-f(z(0))/(z-z(0))=f(z)-0/(z-z(0))=f(z)/(z-z(0)); Not sure where I should with with this proof. Help.
     
  2. jcsd
  3. Sep 10, 2008 #2

    Gib Z

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    Homework Helper

    You started off really good, except you forgot the carry the limit operator through, which is important. Now that you've simplified f'(z(0)), do the same for g'(z(0)) ! Remember to use all the information you're given.
     
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