# use limit definition to prove that the limit is correct

• February 4th 2010, 05:32 PM
redcherry
use limit definition to prove that the limit is correct
$\lim_{x \rightarrow 2 }3=3$
• February 5th 2010, 03:33 AM
HallsofIvy
Quote:

Originally Posted by redcherry
\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:
$\lim_{x\to a}f(x)= L$ if and only if, for every $\epsilon> 0$ there exist $\delta> 0$ such that if $|x-a|< \delta$ then $|f(x)- L|< \epsilon$.

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?