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Math Help - Limit of a constant

  1. #1
    Senior Member BAdhi's Avatar
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    Limit of a constant

    if f(x)=c where c is a constant and it is asked to find

    \lim_{x \to a} f(x) = L

    According to the definition we can take

    \forall \epsilon >0 , \exists\delta>0

    0<|x-a|<\delta \implies |f(x)-L| < \epsilon

    my question is whether \delta and \epsilon are independent from each other
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  2. #2
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    Quote Originally Posted by BAdhi View Post
    if f(x)=c where c is a constant and it is asked to find

    \lim_{x \to a} f(x) = L

    According to the definition we can take

    \forall \epsilon >0 , \exists\delta>0

    0<|x-a|<\delta \implies |f(x)-L| < \epsilon

    my question is whether \delta and \epsilon are independent from each other

    Of course not: \delta almost always depends of \epsilon (and on the function and on what point is x tending

    to, of course), but in this case it's trivially true that L=c\,,\,\,\delta= whatever , as you can easily check.

    Tonio
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  3. #3
    MHF Contributor

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    The largest possible value of \delta depends on \epsilon but \delta can be any number smaller than that largest possible value. For this particular problem, the largest possible value of \delta is infinity (there is no largest possible value).
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