Limits
- Thread starter Nicole5
- Start date
pka
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- Jan 29, 2005
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HallsofIvy
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So this is a "cutesy" way of dealing with the definition of limit:
\(\displaystyle \lim_{x\to a} f(x)= L\) if and only if, given any \(\displaystyle \epsilon> 0\), there exist \(\displaystyle \delta> 0\) such that if \(\displaystyle |x- a|< \delta\) then \(\displaystyle |f(x)- L|< \epsilon\).
Essentially, then, you need to say how to determine \(\displaystyle \delta\) for any given \(\displaystyle \epsilon\).
Okay, Nicole5, since this is your problem, what have you done on it?
Have you, to start with, written out what \(\displaystyle |f(x)- L|< \epsilon\) looks like with f(x)= 2x+ 1 and L= 4?
(Are you sure you have copied the problem correctly? The "target" limit is NOT 4!)
\(\displaystyle \lim_{x\to a} f(x)= L\) if and only if, given any \(\displaystyle \epsilon> 0\), there exist \(\displaystyle \delta> 0\) such that if \(\displaystyle |x- a|< \delta\) then \(\displaystyle |f(x)- L|< \epsilon\).
Essentially, then, you need to say how to determine \(\displaystyle \delta\) for any given \(\displaystyle \epsilon\).
Okay, Nicole5, since this is your problem, what have you done on it?
Have you, to start with, written out what \(\displaystyle |f(x)- L|< \epsilon\) looks like with f(x)= 2x+ 1 and L= 4?
(Are you sure you have copied the problem correctly? The "target" limit is NOT 4!)