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Math Help - Delta-Epsilon proof

  1. #1
    Member
    Joined
    Mar 2008
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    Acolman, Mexico
    Posts
    118

    Delta-Epsilon proof

    I need help with this problem.

    Show that \lim_{x \to c} f(x)=L if and only if \lim_{x \to 0} f(x+c)=L

    Thanks in advance
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  2. #2
    Junior Member
    Joined
    Feb 2010
    Posts
    37

    sufficient condition

    Suppose that lim_{x\rightarrow c}f(x)=L then |x-c|<\delta\rightarrow|f(x)-L|=|f((x-c)+c)<\epsilon, let r=x-c then
    |r-0|<\delta\rightarrow|f(r+c)-L|<\epsilon, ie, lim_{r\rightarrow 0}f(r+c)=L
    I hope you can solve the necessary part now.
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