jueves, 2 de diciembre de 2010

Funcion Exponencial y Logaritmica

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Funcion Racional Cuadratica

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Funcion Racional Lineal

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Funcion Raiz Cuadratica

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Funcion Raiz Lineal

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Funcion Cuadratica

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Funcion Lineal

De todas, ésta es la función menos compleja, ya que no tiene formas, es solamente una recta que cambia de posición conforme se cambian los valores. Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

domingo, 10 de octubre de 2010

Ejercicios de Matemáticas






PROPIEDADES DE LOS NUMEROS
(Escalera)

 1.)\:\qquad x(y+z+w)=xy+xz+xw
                                                

2.)\:\qquad (a+b)(c+d)=a(c+d)+b(c+d)
                    \:\qquad = ac+ad+bc+bd

3.)\:\qquad (7x-3y)^2=(7x-3y)(7x-3y)

\qquad\qquad=7x(7x-3y)-3y(7x-3y)

\qquad\qquad=49x^2-21xy-21yx+9y^2

\qquad\qquad=49x^2-42xy+9y^2            
                

 4.)\:\qquad 5(3x-y)+5(x+5y)-4(2x+y)= 

\qquad\qquad=15x-5y+5x+25y-8x-4y

\qquad\qquad=12x+16y

5.)\:\qquad (7a-2b)(a^2-5ab+2b^2)=

\qquad\qquad=7a(a^2-5ab+2b^2)-2b(a^2-5ab+2b^2)

\qquad\qquad=7a^3-35a^2b+14ab^2-2ba^2+10ab^2-4b^3

\qquad\qquad=7a^3-37a^2b+24ab^2-ab^3

6.)\:\qquad (m^2-m(4m+2n)+n(5-n(m+1)-(7m^2+mn-3n^2)))

\qquad\qquad=(m^2-m(4m2n)+n(5-nm-n-7m^2-mn+3^2))

\qquad\qquad=(m^3-4m^2-2nm+5n-n^2m-n^2-7m^2n-mn^2+3n^2)

\qquad\qquad=m^3-4m^2-2mn+5n-2n^2m+2n^2-7m^2n


SINTAXIS Y SEMANTICA
(Escalera)
1.)\:\qquad ab+c










2.)\:\qquad abc+d













3.)\:\qquad 6x^2-8x+1
 












4.)\:\qquad 7+sen^3{x^2}


















POLINOMIOS
(Escalera)
1.)\:\qquad x^2-3x^2+7x+4

2.)\:\qquad 60x^2-85x-24

3.)\:\qquad xy-3z+2

4.)\:\qquad \frac{12m^2}{n}+\frac{17m}{\sqrt{n}}-14\sqrt{n}

5.)\:\qquad 45x^7+35x^5-8x^3

6.)\:\qquad \frac{3u^3v^4-2u^5v^2+(u^2v^2)^2}{u^3v^2}

                             
ECUACIONES

(Escalera) 
1.)\:\qquad 6z-7=2z+5\qquad\qquad z=3

\qquad\qquad 6(3)-7=2(3)+5

\qquad\qquad 18-7=6+5

\qquad\qquad 11=11
2.)\:\qquad (3x-4)-9x=6x+8     \qquad\qquad x=-1

\qquad\qquad (3(-1)-4)-9(-1)=6(-1)+8

\qquad\qquad (-3-4)+9 = -6 +8

\qquad\qquad -7+9=2

\qquad\qquad 2=2

3.)\:\qquad (x+3)-(3x-1)=0      \qquad\qquad x=2

\qquad\qquad ((2)+3)-(3(2)-1)=0

\qquad\qquad (5)-(6-1)=0

\qquad\qquad 5-5=0

\qquad\qquad 0=0

4.)\:\qquad 5x+3=7x-2       \qquad\qquad x=\frac{5}{2}
        \qquad\qquad 5(\frac{5}{2})+3=7(\frac{5}{2})-2
        \qquad\qquad (\frac{25}{2})+3=(\frac{35}{2})-2
                         \frac{31}{2}=\frac{31}{2}


 5)\:\qquad 12w-7w=2w+1 \qquad w=\frac{1}{3}
                        12(\frac{1}{3}) - 7 (\frac{1}{3}) = 2 (\frac{1}{3}) + 1
                       (\frac{12}{3}) - (\frac{7}{3}) =  (\frac{2}{3}) + 1
                        \frac{5}{3} =  \frac{5}{3}


OPERACIONES ALGEBRAICAS SIMPLIFICAR
(Escalera)


 1)\:\qquad 3a+(2+5a)

\qquad\qquad 3a + 2 + 5a

\qquad\qquad 8a +2
 2)\:\qquad 2x-(2-x)

\qquad\qquad 2x-2+x

\qquad\qquad 3x-2
 3)\:\qquad 5x+ [6-(2x-1)]

\qquad\qquad  5x + [6-2x+1]

\qquad\qquad 5x + 6 - 2x + 1

\qquad\qquad 3x + 7
 4)\:\qquad 3y-[x-2(3x-y)] - [2y-(x+3y)]

\qquad\qquad  3y-[ x -6x + 2y] - [2y-x-3y]

\qquad\qquad  3y-x+6x-2y-2y+x+3y

\qquad\qquad 2y +6x
 5)\:\qquad 15-5[4-2(x+1)]-[3x-5(x+4)]

\qquad\qquad  15-5[4-2x-2]-[3x-5x-20]

\qquad\qquad  15 +20+10x+10 -3x+5x+20

\qquad\qquad 12x +65

ALGEBRA - SIMPLIFICAR
(Escalera)
 1)\:\qquad (-2^2ab^4)^3(a^2b)^5

\qquad\qquad  (64a^3b^1^2) (a^1^0b^5)

\qquad\qquad  64 a^1^3b^1^7

\qquad\qquad
 2)\:\qquad (x^2)(x^3)-(-x^2)(x)

\qquad\qquad  x^5+x^3

\qquad\qquad  

\qquad\qquad
 3)\:\qquad 3x^2(x^3-2x^2+1)

\qquad\qquad  3x^5-6x^4+3x^2

\qquad\qquad  

\qquad\qquad
 4)\:\qquad (2ab^3)^2(-3^2a^2c)^3(-a^4bc^2)^5

\qquad\qquad  (4a^2^6)(729 a^6c^3)(-a^2^0b^5c^1^0)

\qquad\qquad  -2916 a^5^2b^5c^1^3

\qquad\qquad

 5)\:\qquad -2a^2b(a^3+5a^2b^2-3b^4)

\qquad\qquad  -2a^5b -10a^4b^3+6a^2b^4

\qquad\qquad  

\qquad\qquad
 MULTIPLICACION DE POLINOMIOS
(Escaleras)
 1)\:\qquad (x+7)(x-3)

\qquad\qquad x(x-3)+7(x-3)

\qquad\qquad x^2 - 3x +7x-21

\qquad\qquad x^2+4x-21
 2)\:\qquad (2x-5)(x+7)

\qquad\qquad 2x(x+7)-5(x+7)

\qquad\qquad 2x^2 +14x-5x-35

\qquad\qquad 2x^2 +9x-35
 3)\:\qquad (x+2)(x-4) -x(x-2)

\qquad\qquad x(x-4)+2(x-4)-x(x-2)

\qquad\qquad x^2-4x+2x-8-x^2+2x

\qquad\qquad  -8

 4)\:\qquad (2x-1)(4x^2+2x+1)

\qquad\qquad 2x(4x^2+2x+1)-1(4x^2+2x+1)

\qquad\qquad 8x^3+4x^2+2x-4x^2-2x-1

\qquad\qquad  8x^3-1
 5)\:\qquad (x-2y)(x^2+2xy+4y^2)

\qquad\qquad x(x^2+2xy+4y^2)-2y(x^2+2xy+4y^2)

\qquad\qquad x^3 +2x^2y +4y^2x -2yx^2-4xy^2-8y^3

\qquad\qquad x^3 -8y^3
EFECTUAR OPERACIONES CON FRACCIONES
(Escaleras)
 1)\:\qquad (\frac{6x^2y^3z}{8xy^3z^2})^3

\qquad\qquad 

\qquad\qquad 

\qquad\qquad
                      \qquad\qquad (\frac{216x^6y^9z^3}{512x^3y^9z^6})

\qquad\qquad 

\qquad\qquad
                      \qquad\qquad (\frac{216x^3}{512z^3})

\qquad\qquad 

\qquad\qquad

 2)\:\qquad \frac{-44a^3b^2}{66a^5b^8}

\qquad\qquad 

\qquad\qquad 

\qquad\qquad
                       \:\qquad \frac{-44}{66a^2b^6}

\qquad\qquad 

\qquad\qquad 

\qquad\qquad
 3)\:\qquad \frac{x^6y^4}{x^3y^2}

\qquad\qquad 

\qquad\qquad 

\qquad\qquad
                       \:\qquad x^3y^2

\qquad\qquad 

\qquad\qquad 

\qquad\qquad
FACTORIZACION POR FACTOR COMUN
(Escaleras)
 1)\:\qquad 7xy+2xz

\qquad\qquad x(7y+2z)

\qquad\qquad 

\qquad\qquad
 2)\:\qquad 4xy-6xz+8xw

\qquad\qquad 2x(2y-3z+4w)

\qquad\qquad 

\qquad\qquad
 3)\:\qquad 5a^5b^4-10a^3b^6+20a^2b^8

\qquad\qquad 5a^2b^4(a^3-2ab^2+4b^4)

\qquad\qquad 

\qquad\qquad
 4)\:\qquad x^3-9x^2+2x-18

\qquad\qquad x^2(x-9)+2(x-9)

\qquad\qquad (x-9)(x^2+2)

\qquad\qquad
 5)\:\qquad x^3+4x^2y+xy^2+4y^2

\qquad\qquad x^3+xy^2+4x^2y+4y^2

\qquad\qquad xy(x^2+y)+4y(x^2+y)

\qquad\qquad (x^2+y)(xy+4y)
 6)\:\qquad 7x^2-14x-6x+12

\qquad\qquad 7x(x-2)-6(x-2)

\qquad\qquad (x-2)(7x-6)

\qquad\qquad
FACTORIZACION DE TRINOMIOS
(Escaleras)
 1)\:\qquad x^2-x-6

\qquad\qquad (x+2)(x-3)

\qquad\qquad 

\qquad\qquad




 2)\:\qquad x^2+2x-8

\qquad\qquad (x-2)(x+4)

\qquad\qquad 

\qquad\qquad
 3)\:\qquad  x^2-4x-21

\qquad\qquad (x+3)(x-7)

\qquad\qquad 

\qquad\qquad
 4)\:\qquad  5x^2-14x-3

\qquad\qquad (x-3)(5x+1)

\qquad\qquad 

\qquad\qquad
 5)\:\qquad  5x^2-17x+6

\qquad\qquad (x-3)(5x-2)

\qquad\qquad 

\qquad\qquad
 6)\:\qquad  7x^2-20x+12

\qquad\qquad (x-2)(7x-6)

\qquad\qquad 

\qquad\qquad

FACTORIZACION CON FRACCIONES
(Escaleras)


 1)\:\qquad  \frac{9x^2-6xy-12y^2}{3xy}

\qquad\qquad 

\qquad\qquad 

\qquad\qquad
          \:\qquad  \frac{3x}{y} - \frac{2}{1}-\frac{6y}{x}

\qquad\qquad 

\qquad\qquad 

\qquad\qquad
 2)\:\qquad  \frac{2a^4b-4a^3b^2+2a^2b^3}{2a^2b}

\qquad\qquad 

\qquad\qquad 

\qquad\qquad
         \:\qquad  \frac{a^2-2ab+b^2}{1} 

\qquad\qquad 

\qquad\qquad 

\qquad\qquad
         \:\qquad  \frac{(a-b)(a+b)}{1} 

\qquad\qquad 

\qquad\qquad 

\qquad\qquad
 3)\:\qquad  \frac{a^3b^3-2a^2b^4-15ab^5}{ab^3}

\qquad\qquad 

\qquad\qquad 

\qquad\qquad
         \:\qquad  \frac{a^2-2ab-15b^2}{1} 

\qquad\qquad 

\qquad\qquad 

\qquad\qquad
         \:\qquad  \frac{(a-5b)(a+3b)}{1} 

\qquad\qquad 

\qquad\qquad 

\qquad\qquad
        
 4)\:\qquad  \frac{6x^2-7x-5}{3x^2-2x-5}

\qquad\qquad 

\qquad\qquad 

\qquad\qquad
         \:\qquad  \frac{(2x+1)(3x-5)}{(3x-5)(x+1)} 

\qquad\qquad 

\qquad\qquad 

\qquad\qquad
         \:\qquad  \frac{2x+1}{x+1} 

\qquad\qquad 

\qquad\qquad 

\qquad\qquad
 5)\:\qquad  \frac{12y^2+3y}{20y^2+9y+1}

\qquad\qquad 

\qquad\qquad 

\qquad\qquad
         \:\qquad  \frac{3y(4y+1)}{(5y+1)(4y+1)} 

\qquad\qquad 

\qquad\qquad 

\qquad\qquad
         \:\qquad  \frac{3y}{5y+1} 

\qquad\qquad 

\qquad\qquad 

\qquad\qquad

FORMULA GENERAL

 ax^2+bx+c=0
 (\frac{1}{a})(ax^2+bx+c)=(0)(\frac{1}{a})
 x^2+\frac{b}{a}x=-\frac{c}{a}
 x^2+\frac{b}{a}x+(\frac{b}{2a})^2=-\frac{c}{a}+(\frac{b}{2a})^2
 x^2+\frac{b}{a}x+\frac{b^2}{4a^2} =-\frac{c}{a}+\frac{b^2}{4a^2}
 (x+\frac{b}{2a})^2 =\frac{b^2-4ac}{4a^2}
 \sqrt{(x+\frac{b}{2a})^2} = \frac{+}{}\sqrt{\frac{b^2-4ac}{4a^2}}
 x+\frac{b}{2a} = \frac{+}{}\sqrt{\frac{b^2-4ac}{4a^2}}
 x =-\frac{b}{2a} \frac{+}{}\sqrt{\frac{b^2-4ac}{4a^2}}
 x =-\frac{b}{2a}+\frac{1}{2a} \frac{+}{}\sqrt{b^2-4ac}
 x =\frac{-b\frac{+}{}\sqrt{b^2-4ac}}{2a}