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Please use this identifier to cite or link to this item: http://acervodigital.unesp.br/handle/unesp/360565
Title: 
Area under the exponential curve
Author(s): 
Arik, Okay
Language: 
eng
Description: 
  • Area, Calculus, Curves and Exponential Functions
  • Consider a curve consisting of segments joining the points(n/k,an), where an=(1-1/k)^n and n=1,2,3,... . The region under this curve is broken into triangular pieces by extending the segments to the x axis. Each extended segment projects onto a segment of length 1 on the x axis because an/(k(an-an+1))=1 You can align these triangles one on top of the other above the interval [0,1] on the x axis using the "align" slider. You can control the constant using the "triangles per unit length" slider. Let x=n/k. As n and k tend to infinity, the curve approaches the exponential curve y=e^(-x). The "total length" slider controls the length of the x interval. As the total length tends to infinity, the aligned triangles fill the unit square of area 1
  • Componente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemática
Issue Date: 
  • 8-Sep-2008
  • 8-Sep-2008
  • 2008
  • 8-Sep-2008
  • 7-Sep-2008
Publisher: 
Wolfram Demonstration Project
Keywords: 
  • Exponential functions
  • Area
  • Curves
  • Educação Superior::Ciências Exatas e da Terra::Matemática::Análise Funcional
Credits: 
This demonstration needs the "MathematicaPlayer.exe" to run. Found in http://objetoseducacionais2.mec.gov.br/handle/mec/4737
Source: 
http://objetoseducacionais2.mec.gov.br/handle/mec/5127
URI: 
http://acervodigital.unesp.br/handle/unesp/360565
Rights: 
Demonstration freeware using Mathematica Player
Type: 
outro
Appears in Collections:MEC - Objetos Educacionais (BIOE) - OE

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