9893
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Bolzano's Theorem
Bolzano's theorem states that if
is a continuous function in the closed interval
with
and
of opposite sign, then there is a
in the open interval
such that
.
Contributed by:
Julio Cesar de la Yncera
SNAPSHOTS
DETAILS
Snapshot 1: The function is positive in the interval and therefore
for all
in
.
Snapshot 2: The function is negative in the interval so
for all
in
.
Snapshot 3: The function is positive for
and negative for
, therefore there is a
in
such that
.
RELATED LINKS
Bolzano's Theorem
(
Wolfram
MathWorld
)
Bolzano-Weierstrass Theorem
(
Wolfram
MathWorld
)
Weierstrass Intermediate Value Theorem
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Bolzano's Theorem
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/BolzanosTheorem/
Contributed by:
Julio Cesar de la Yncera
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
Fermat's Theorem on Stationary Points
Julio Cesar de la Yncera
Cauchy Mean-Value Theorem
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Two Integral Mean Value Theorems
Soledad María Sáez Martínez and Félix Martínez de la Rosa
Two Integral Mean Value Theorems of Flett Type
Soledad María Sáez Martínez and Félix Martínez de la Rosa
Marden's Theorem
Bruce Torrence
Squeeze Theorem
Bruce Atwood (Beloit College)
Lucas-Gauss Theorem
Bruce Torrence
2D and 3D Views of the Weierstrass Function
Daniel de Souza Carvalho
Bolzano's Function
Izidor Hafner
Bolzano's Continuous but Nowhere Differentiable Function
Izidor Hafner
Related Topics
Analysis
Calculus
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+