| dc.contributor | Universidade Estadual Paulista (UNESP) | |
| dc.creator | Martínez, Soledad | |
| dc.creator | Rosa, Félix | |
| dc.date | 2011-05-26T19:54:52Z | |
| dc.date | 2011-05-26T19:54:52Z | |
| dc.date | 2011-05-26 | |
| dc.date.accessioned | 2017-04-05T17:01:54Z | |
| dc.date.available | 2017-04-05T17:01:54Z | |
| dc.identifier | http://acervodigital.unesp.br/handle/123456789/4532 | |
| dc.identifier | http://objetoseducacionais2.mec.gov.br/handle/mec/7263 | |
| dc.identifier.uri | http://repositorioslatinoamericanos.uchile.cl/handle/2250/831943 | |
| dc.description | Exponents and Logarithms, inequalities, area, trapezoid, y = 1/x | |
| dc.description | The arithmetic-logarithmic-geometric mean inequality states that if 0<a<b then sqrt(ab) < (b-a)/(lnb – lna) < (a+b)/2
Left graphic:
The area under y = 1/x on the interval (a,b) is lnb - lna
The area under the tangent at x = (a+b)/2 is 2(b-a)/(a+b)
Then lnb – lna > 2(b-a)/(a+b)
Right graphic:
The area under y = 1/x on the interval (a,b) is lnb - lna, as in the left graphic.
The area of the left trapezoid is ½(1/a + 1/(sqrt(ab)))(sqrt(ab) - a) = (b-a)/2sqrt(ab)
The area of the right trapezoid is ½(1/b + 1/(sqrt(ab)))(b - sqrt(ab)) = (b-a)/2sqrt(ab)
Then lnb – lna < (b-a)/sqrt(ab) | |
| dc.description | Componente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemática | |
| dc.publisher | Wolfram Demonstration Project | |
| dc.relation | TheArithmeticLogarithmicGeometricMeanInequality.nbp | |
| dc.rights | Demonstration freeware using Mathematica Player | |
| dc.subject | Arithmetic | |
| dc.subject | Logarithmic | |
| dc.subject | Aritmética | |
| dc.subject | Logaritmo | |
| dc.subject | Educação Superior::Ciências Exatas e da Terra::Matemática::Álgebra | |
| dc.title | The arithmetic-logarithmic-geometric mean inequality | |
| dc.type | Software | |
