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Cálculo de limites de funciones polinomicas,
Cálculo de limites de funciones racionales y
Limite de funciones racionales e...
Definiciones clave.
 Racional.- Numero puede representarse como el cociente
de dos números enteros con denominador distin...
Definiciones clave.
 Infinito.- Infinito no tiene final. Es la idea de que algo
que no termina.
Cálculo de limites de fun...
CÁLCULO DE
LIMITES DE
FUNCIONES
POLINOMICAS
Las funciones polinomicas son aquellas cuya
expresión es un polinomio, como por ejemplo,
f(x)=3x4-5x+6.
Se trata de funcio...
Una función polinomial tiene la forma:
P(x) = c0 + c1x + c2x2 +···+cnxn
donde c0,c1,...,cn son números reales llamados coe...
Para cada número real x, f(x) toma un valor
real, entonces el dominio de una función
polinomial cualquiera, es el conjunto...
Cálculo de limites de funciones polinomicas
Ejemplos:
CÁLCULO DE
LIMITES DE
FUNCIONES
RACIONALES
Una función racional es el cociente de dos polinomios.
Una función racional es una función de la forma:
R(x) = P(x)
Q(x)
C...
Dominio de una Función Racional
Una función racional f(x) no está definida para valores
de x que anulen el denominador, pe...
Estrategias para calcular limites a funciones racionales
2.- Si el limite f(x) cuando x tiende a
c, no puede evaluarse por...
Cálculo de limites de funciones racionales
Ejemplos:
LIMITES DE
FUNCIONES
RACIONALES
EN EL INFINITO
• El límite de una función racional cuando x
 +- infinito es igual al límite del cociente
de los términos de mayor grado ...
• El valor de este límite depende del valor que tengan n y m:
• Si el grado del numerador es mayor que el grado del
denomi...
Limite de funciones racionales en el infinito
Ejemplo:
APLICACIÓN
COTIDIANA
Aplicación Cotidiana
Las funciones están presentes en la vida cotidiana:
«espacio que recorre un móvil en función del
tiem...
CONCLUSIONES
Conclusiones
En los temas anteriores vimos el uso del algebra para encontrar
el limite de una función, y que muchas veces ...
Fuentes consultadas.
• http://www.disfrutalasmatematicas.com/definiciones/polinomio.h
tml
• http://definicion.de/racional/...
Cálculo de limites de funciones polinómicas, racionales y en el infinito.
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Cálculo de limites de funciones polinómicas, racionales y en el infinito.

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Tema: Cálculo de limites de funciones Polinómicas.
Cálculo de limites de funciones racionales.
Limite de funciones racionales en el Infinito.
Asignatura: Cálculo Diferencial e Integral.

Universidad Politécnica de Victoria.
2013

Published in: Education
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Cálculo de limites de funciones polinómicas, racionales y en el infinito.

  1. 1. Cálculo de limites de funciones polinomicas, Cálculo de limites de funciones racionales y Limite de funciones racionales en el infinito Definiciones clave.  Limite de una función.- Valor hacia donde tiende la variable dependiente cuando el valor de la variable independiente se acerca a un valor fijo.  Función.- Relación entre dos conjuntos X y Y, tal que cada elemento de X le corresponda uno y solamente uno de los elementos de Y.
  2. 2. Definiciones clave.  Racional.- Numero puede representarse como el cociente de dos números enteros con denominador distinto de cero.  Polinomio.- Expresión hecha con constantes, variables y exponentes, que están combinados usando sumas, restas y multiplicaciones, pero no divisiones. Los exponentes sólo pueden ser 0,1,2,3, etc. . Cálculo de limites de funciones polinomicas, Cálculo de limites de funciones racionales y Limite de funciones racionales en el infinito
  3. 3. Definiciones clave.  Infinito.- Infinito no tiene final. Es la idea de que algo que no termina. Cálculo de limites de funciones polinomicas, Cálculo de limites de funciones racionales y Limite de funciones racionales en el infinito
  4. 4. CÁLCULO DE LIMITES DE FUNCIONES POLINOMICAS
  5. 5. Las funciones polinomicas son aquellas cuya expresión es un polinomio, como por ejemplo, f(x)=3x4-5x+6. Se trata de funciones continuas cuyo dominio es el conjunto de los números reales. Cálculo de limites de funciones polinomicas
  6. 6. Una función polinomial tiene la forma: P(x) = c0 + c1x + c2x2 +···+cnxn donde c0,c1,...,cn son números reales llamados coeficientes del polinomio; n∈N es un número natural que, si cn , 0, se llama grado del polinomio. Cálculo de limites de funciones polinomicas
  7. 7. Para cada número real x, f(x) toma un valor real, entonces el dominio de una función polinomial cualquiera, es el conjunto de todos los números reales. Cálculo de limites de funciones polinomicas
  8. 8. Cálculo de limites de funciones polinomicas Ejemplos:
  9. 9. CÁLCULO DE LIMITES DE FUNCIONES RACIONALES
  10. 10. Una función racional es el cociente de dos polinomios. Una función racional es una función de la forma: R(x) = P(x) Q(x) Cálculo de limites de funciones racionales
  11. 11. Dominio de una Función Racional Una función racional f(x) no está definida para valores de x que anulen el denominador, pero si para los demás números reales, así que su dominio consiste en el conjunto de todos los números reales para los cuales el denominador sea distinto de cero. Cálculo de limites de funciones racionales
  12. 12. Estrategias para calcular limites a funciones racionales 2.- Si el limite f(x) cuando x tiende a c, no puede evaluarse por sustitución directa, realizar manipulación algebraica. Cálculo de limites de funciones racionales 1.- Aprende a reconocer los limites calculables por sustitución directa.
  13. 13. Cálculo de limites de funciones racionales Ejemplos:
  14. 14. LIMITES DE FUNCIONES RACIONALES EN EL INFINITO
  15. 15. • El límite de una función racional cuando x  +- infinito es igual al límite del cociente de los términos de mayor grado del numerador y denominador. Limite de funciones racionales en el infinito
  16. 16. • El valor de este límite depende del valor que tengan n y m: • Si el grado del numerador es mayor que el grado del denominador (n > m), el límite es +- infinito, dependiendo de que los signos de los cocientes an y bm sean iguales o distintos. • Si el grado del numerador es igual que el grado del denominador (n = m), • Si el grado del numerador es menor que el grado del denominador (n<m), el límite es 0. Limite de funciones racionales en el infinito
  17. 17. Limite de funciones racionales en el infinito Ejemplo:
  18. 18. APLICACIÓN COTIDIANA
  19. 19. Aplicación Cotidiana Las funciones están presentes en la vida cotidiana: «espacio que recorre un móvil en función del tiempo», «crecimiento de una planta en función del tiempo», «costo de cierto papel en función de la cantidad», «aumento o disminución de la temperatura del agua en función del tiempo»
  20. 20. CONCLUSIONES
  21. 21. Conclusiones En los temas anteriores vimos el uso del algebra para encontrar el limite de una función, y que muchas veces nos simplifica el resolver dicho problemas. Las funciones racionales son continuas en todos los números reales, excepto en aquellos que hacen cero su denominador. Son continuas en su dominio, que excluye dichos puntos.
  22. 22. Fuentes consultadas. • http://www.disfrutalasmatematicas.com/definiciones/polinomio.h tml • http://definicion.de/racional/ • http://iescastelar.juntaextremadura.net/web/departamentos/mat ematicas/matematicasccss2ba/matematicas2ccss/tlimitesintrod uccion.htm • http://mimosa.pntic.mec.es/jgomez53/matema/docums/perez- calculo1.pdf • http://www.conevyt.org.mx/bachillerato/material_bachilleres/cb6/ 5sempdf/cad2pdf/calculo1_fasc2.pdf

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