Finite Limit at a Finite Point

ε

lim

xc

f(x) = L

●

ε = 1

δ

1

= 2.02775

δ

2

= 3.08601

automatically calculate δ values

The function

f(x)

has a finite limit,

L

, as

xc

. This means that for any

ε>0

, there is an interval of width

δ

1

+

δ

2

around

c

(perhaps with

δ

1

and

δ

2

very small), such that

|f(x)-L|<ε

whenever

x

is in that interval. Move the point directly and adjust

ε

using the slider. This Demonstration computes the largest

δ

1

and

δ

2

for a given

ε

so that

f(x)

lies between

L-ε

and

L+ε

. The values for

δ

1

and

δ

2

may be found automatically or manually by dragging. The function shown is

f(x)=3

1/3

(x-1)

-2

.