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Thread: use limit definition to prove that the limit is correct

  1. #1
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    use limit definition to prove that the limit is correct

    $\displaystyle \lim_{x \rightarrow 2 }3=3$
    Last edited by mr fantastic; Feb 5th 2010 at 12:25 PM. Reason: Added the latex tags and fixed latex.
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  2. #2
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    Quote Originally Posted by redcherry View Post
    \lim_{x\rightarrow \2 }3=3
    Have you tried anything at all? This is just about the easiest problem you are ever going to have!

    The "limit definition" you refer to is:
    $\displaystyle \lim_{x\to a}f(x)= L$ if and only if, for every $\displaystyle \epsilon> 0$ there exist $\displaystyle \delta> 0$ such that if $\displaystyle |x-a|< \delta$ then $\displaystyle |f(x)- L|< \epsilon$.

    Here f(x) is the constant function, 3 and L= 3 so for all x, |f(x)-L|= |3-3|=0. What does that tell you?
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