$\displaystyle \lim_{x \rightarrow 2 }3=3$

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- Feb 4th 2010, 05:32 PMredcherryuse limit definition to prove that the limit is correct
$\displaystyle \lim_{x \rightarrow 2 }3=3$

- Feb 5th 2010, 03:33 AMHallsofIvy
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?