Calculo

CÁLCULO DIFERENCIAL E INTEGRAL Impartido por: Gloria Angélica Fuentes Zenteno

UNIDAD I ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

UNIDAD II ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

UNIDAD III ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object]

Preliminares ,[object Object],[object Object]

El sistema de los números reales ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Propiedades de campo ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Propiedades del orden ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Simplifique todo lo que sea posible ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Ejercicios resueltos ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Resolver los ejercicos pares. Entregar

Realice las operaciones indicadas y simplifique ,[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Desigualdades ,[object Object],[object Object],[object Object]

Tipos de intervalos ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Tarea: Exprese el Conjunto solución ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Valor absoluto ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Tarea: Encuentre el conjunto solución de la desigualdad ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Aunque el cálculo fue descubierto a fines del siglo XVII, sus fundamentos permanecieron en estado de confusión y desorden hasta que Cauchy y sus contemporáneos impusieron normas de rigor. Debemos a Cauchy la idea de basar el cálculo en una clara definición del concepto de límite. Tarea: Biografía de Cauchy

Funciones y límites ,[object Object],[object Object],[object Object],A B C D E 1 2 3 4 5 A B C D E 1 2 3 4 5

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Si F( x ) = x 2 - 2 x => F( 4 )= ( 4 ) 2 - 2( 4 ) = 16-8 = 8 F( 4+h )= ( 4+h ) 2 - 2( 4+h ) = 16+8h+h 2 -(8+h) = 16+8h+h 2 -8-h = h 2 +7h+8 F(4+h) - F(4) = h 2 +7h+8 – 8 = h 2 +7h F(4+h)-F(4) / h = (h2+7h) / h = h(h+7) / h = h+7

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Operaciones con funciones ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Clasificación parcial de funciones

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Introducción a los límites ,[object Object],Noción intuitiva Considere la función determinada por la fórmula F(x)= (x 3 -1)/(x-1). Comencemos analizando la gráfica de la función; tabulemos : x -1 -½ 0 1 2 f(-1)= ((-1) 3 -1)/((-1)-1)=(-1-1)/(-1-1)= -2/-2 = +1 y +1 0.75 1  7 f(½) = ((-½) 3 -1) / ((-½)-1)=(- 1 / 8 – 8 / 8 ) / (-½- 2 / 2 )= - 9 / 8 / - 3 / 2 =+0.75 f(1)= ((1) 3 -1)/((1)-1)=(1-1)/(1-1)= 0/0 = Indeterminado Graficando lo tabulado: ¿Qué pasa de 0 a 2?

[object Object],[object Object],[object Object],[object Object],Podemos concluir que el límite de f(x)= (x 3 -1)/(x-1) = 3; Pero, en ésta forma es erroneo. Necesitamos aplicar el límite, en el punto donde la función no existe. Lim f(x)= lim (x 3 -1)/(x-1) x -> 1 x -> 1 =lim (x 2 +x+1)(x-1)/(x-1) x -> 1 =lim (x 2 +x+1) = 1 2 +1+1 x -> 1 = 3 Significado intuitivo de límite Def.: Decir que lim f(x)=L significa que cuando x está cerca, pero difiere de c, f(x) está cerca de L. => Decir que lim f(x)=3, significa que cuando x está cerca de uno, pero no es uno, f(x) está cerca de 3, pero no es 3.

Ejemplos: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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