10182
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Discontinuity
For a value
, let
=
(the limit from the left) and
=
(the limit from the right).
If
L
^{-}
=
L
^{+}
=
, the function is continuous at
.
If
L
^{-}
=
L
^{+}
≠
, the function has a removable discontinuity at
.
If
L
^{-}
≠
L
^{+}
, and both values are finite, the function has a jump discontinuity at
.
If
L
^{-}
≠
L
^{+}
, and one or both values is infinite, the function has an infinite discontinuity at
. This is also called an essential discontinuity.
Contributed by:
Ed Pegg Jr
THINGS TO TRY
Slider Zoom
SNAPSHOTS
RELATED LINKS
Discontinuity
(
Wolfram
MathWorld
)
Discontinuous
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Discontinuity
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/Discontinuity/
Contributed by:
Ed Pegg Jr
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Riemann's Example of a Continuous but Nowhere Differentiable Function
Michael Trott
Boole Differential Equation with Continued Fractions
Andreas Lauschke
Lipschitz Continuity
Bruce Atwood
Cauchy Mean-Value Theorem
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
The Generalized Weierstrass-Riemann Functions
Michael Croucher
Riemann versus Lebesgue
Francisco J. Freniche
Bisection Method
Edda Eich-Soellner (University of Applied Sciences, München, Germany)
Orbits of the Tent Function's Iterates
Bernard Vuilleumier
Squeeze Theorem
Bruce Atwood (Beloit College)
Haar Function Interval Points
Michael Schreiber
Related Topics
Analysis
Calculus
College Mathematics
High School Calculus and Analytic Geometry
High School Mathematics
High School Precalculus
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+