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

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

Compare with uniform continuity.

Interactive Real Analysis, ver. 1.9.5
(c) 1994-2007, Bert G. Wachsmuth
Page last modified: Mar 28, 2007