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Homework Help: Limit theorems

  1. Oct 31, 2007 #1
    1. The problem statement, all variables and given/known data

    prove that if [tex]lim_{x\rightarrow c}[/tex] f(x) = L, then there are positive numbers A and B such that if 0 < |x-c|< A, then |f(x)|< B

    2. The attempt at a solution

    i know it's something to do with the limit definition, where for [tex]\epsilon[/tex] > 0, there exists a [tex]\delta[/tex] > 0 such that 0 < |x-c| < [tex]\delta[/tex], then |f(x)-L| < [tex]\epsilon[/tex]

    i don't know how to get my way through proving it!
    please helpppp!
  2. jcsd
  3. Oct 31, 2007 #2


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    Homework Helper

    yes, precisely, use the definition of a limit. Your task is to identify what delta and epsilon will make it works
  4. Oct 31, 2007 #3


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    Science Advisor
    Homework Helper

    Pick a B>L. Pick epsilon=B-L. Use the definition of limit to find a delta. Set A=delta.
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