# Sine Wave Example of the Epsilon-Delta Definition of Limit

Sine Wave Example of the Epsilon-Delta Definition of Limit

This Demonstration illustrates the - definition for the limit of the sinusoid as tends to . You can vary the amplitude , the frequency , and the value of interest, . Then, for each chosen value for , you can find a valid , i.e., a such that whenever , . When a valid has been found, the vertical sides of the box appear green. For an invalid , the vertical sides of the box appear red.

ϵ

δ

L

f(x)=bsin(2πcx)

x

a

b

c

x

a

ϵ

δ

δ

|x-a|<δ

|f(x)-L|<ϵ

δ

(ϵ,δ)

δ

(ϵ,δ)