A Case of the Epsilon-Delta Definition of a Limit
A Case of the Epsilon-Delta Definition of a Limit
From the intuitive notion of a limit, if f(x)=L, then can be made as close to as desired simply by finding an that is sufficiently close to . The formalized version of this is the definition of a limit. In this case x+3=5. Select a value for and you can find a corresponding so that, if , then .
lim
xa
f(x)
L
x
a
ϵ-δ
lim
x4
1
2
ϵ>0
δ>0
0<|x-a|<δ
|f(x)-L|<ϵ
Details
Details
Snapshot 1: Select an .
ϵ
Snapshot 2: Find a corresponding .
δ
Snapshot 3: Close in on the limit.
Permanent Citation
Permanent Citation
Joseph F. Kolacinski
"A Case of the Epsilon-Delta Definition of a Limit"
http://demonstrations.wolfram.com/ACaseOfTheEpsilonDeltaDefinitionOfALimit/
Wolfram Demonstrations Project
Published: October 24, 2007