Sine Wave Example of the Epsilon-Delta Definition of Limit

sine wave amplitude

1

sine wave frequency

1

2π

x value of interest (

a

)

π

2

epsilon (ϵ)

0.5

delta (δ)

0.358

This Demonstration illustrates the

ϵ

-

δ

definition for the limit

L

of the sinusoid

f(x)=bsin(2πcx)

as

x

tends to

a

. You can vary the amplitude

b

, the frequency

c

, and the

x

value of interest,

a

. Then, for each chosen value for

ϵ

, you can find a valid

δ

, i.e., a

δ

such that whenever

|x-a|<δ

,

|f(x)-L|<ϵ

. When a valid

δ

has been found, the vertical sides of the

(ϵ,δ)

box appear green. For an invalid

δ

, the vertical sides of the

(ϵ,δ)

box appear red.