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Epsilon Delta Definition Visualization

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Seeing the Epsilon-Delta Definition of a Limit

Given f(x), c and ϵ, use the δ-slider to find a δ and a limit value L with limxcf(x)=L such that for the given ϵ, if |xc|<δ then |f(x)L|<ϵ.

 

f(x)=52x,c=2

ε = 0.3, δ = 1.5

limxcf(x)=     δ=         

Use the slider to explore the values of δ that might work for the given value of ϵ.

Looking at this diagram, what does it mean to say "Given ϵ>0, choose δ>0 such that if |xc|<δ then |f(x)L|<ϵ"?  This means that if you restrict the x-values allowed to be within the two vertical lines, then the graph will not go below the lower horizontal line or above the upper horizontal line.  Being between the two vertical lines is the same as saying |xc|<δ and being between the two horizontal lines is the same as saying |f(x)L|<ϵ.

 

 


This page titled Epsilon Delta Definition Visualization is shared under a CC BY license and was authored, remixed, and/or curated by Larry Green.

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