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)