Math 125-103
Fall 2012
Quiz 8, Sept. 12
Carter
Name
Give the -δ definition of a limit. That is define precisely what is meant by the sentence,
“ lim f (x) = L.”
x→c
Solution: We say that limx→c f (x) = L if and only if for every > 0 there is a δ > 0 such that
|f (x) − L| < provided
|x − c| < δ.
In more symbols, limx→c f (x) = L if and only if ∀ > 0, ∃δ > 0 such that
|f (x) − L| < provided
|x − c| < δ.