# Finite Limit at a Finite Point

Finite Limit at a Finite Point

The function has a finite limit, , as . This means that for any , there is an interval of width + around (perhaps with and very small), such that whenever is in that interval. Move the point directly and adjust using the slider. This Demonstration computes the largest and for a given so that lies between and . The values for and may be found automatically or manually by dragging. The function shown is .

f(x)

L

xc

ε>0

δ

1

δ

2

c

δ

1

δ

2

|f(x)-L|<ε

x

ε

δ

1

δ

2

ε

f(x)

L-ε

L+ε

δ

1

δ

2

f(x)=3-2

1/3

(x-1)