Java Applet: Illustrating Continuity

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This graph shows the function

f(x) = x⁴ + 0.5 if x < 1
f(x) = 0.5 x + 1 if 1 x < 2
f(x) = cos( x) + 1 if 2 x

To use the Java applet:

Click on Options for control panel
Select x by clicking on the x-axis
Select a given epsilon
Guess delta and press Apply

If for any given epsilon value you can find a positive delta value such that the red area touches the graph inside the green area, then your function is continuous at the given values of x

Your browser can not handle Java Applets ...

This graph shows the function

f(x) = x² + 1.3 if x < 1
f(x) = sin(x - 1) + 2 if 1 x

To use the Java applet:

Click on Options for control panel
Select x by clicking on the x-axis
Select a given epsilon
Guess delta and press Apply

If for any given epsilon value you can find a positive delta value such that the red area touches the graph inside the green area, then your function is continuous for x = c

The first function is continous for all x, while the second function is not continuous for x = 1 and continuous for all other x.

Compare with uniform continuity.

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