# 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