A Case of the Epsilon-Delta Definition of a Limit

​
ϵ
2
δ
4
From the intuitive notion of a limit, if
lim
xa
f(x)=L
, then
f(x)
can be made as close to
L
as desired simply by finding an
x
that is sufficiently close to
a
. The formalized version of this is the
ϵ-δ
definition of a limit. In this case
lim
x4
1
2
x+3=5
. Select a value for
ϵ>0
and you can find a corresponding
δ>0
so that, if
0<|x-a|<δ
, then
|f(x)-L|<ϵ
.

Details

Snapshot 1: Select an
ϵ
.
Snapshot 2: Find a corresponding
δ
.
Snapshot 3: Close in on the limit.

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