análisis-matemático

Teorema:

Sea a_{n} acotada ==>

Si [An][ |b_{n}| [< |a_{n}+c| ] ==> b_{n} está acotada

Demostración:

Sea a_{n} acotada ==>

[EN][ |a_{n}| [< N ]

|b_{n}| [< |a_{n}+c| [< |a_{n}|+|c| [< N+|c|

Se define M = N+|c| ==>

|b_{n}| [< M

Teorema:

[An][ 0 [< e^{n} & 0 [< e^{(-n)} ]

Demostración:

por inducción:

0 [< 1 = e^{0}

0 [< 1 [< e^{n} [< e^{n+1}

Por descenso:

0 = (1/e^{oo}) = ( 1/oo^{[e]+(-1)} ) = (1/oo)

0 [< (1/e^{n}) [< (1/e^{n+(-1)})

Teorema:

Sea a_{n} acotada ==>

Si [An][ |b_{n}| [< |e^{|a_{n}|}+c| ] ==> b_{n} está acotada

Demostración:

Sea a_{n} acotada ==>

[EN][An][ |a_{n}| [< N ]

e^{|a_{n}|} [< e^{N}

|b_{n}| [< |e^{|a_{n}|}+c| [< |e^{|a_{n}|}|+|c| = e^{|a_{n}|}+|c| [< e^{N}+|c|

Se define M = e^{N}+|c| ==>

|b_{n}| [< M

Teorema:

F(x,t) = ( x(t) )^{p+1}+(-1)·h(t)·( x(t)+(-1)·M(t) )

h(t) = (p+1)·( M(t) )^{p}

Demostración:

d_{x}[ F(x,t) ] = d_{x}[ ( x(t) )^{p+1}+(-1)·h(t)·( x(t)+(-1)·M(t) ) ] = ...

... d_{x}[ ( x(t) )^{p+1} ]+d_{x}[ (-1)·h(t)·( x(t)+(-1)·M(t) ) ] = ...

... d_{x}[ ( x(t) )^{p+1} ]+(-1)·h(t)·d_{x}[ x(t)+(-1)·M(t) ] = ...

... d_{x}[ ( x(t) )^{p+1} ]+(-1)·h(t)·( d_{x}[ x(t) ]+d_{x}[ (-1)·M(t) ] ) = ...

... (p+1)·( x(t) )^{p}+(-1)·h(t) = 0

Teorema:

F(x,t) = e^{(p+1)·x(t)}+(-1)·h(t)·( e^{x(t)}+(-1)·M(t) )

h(t) = (p+1)·( M(t) )^{p}

Teorema:

F(x,y,t) = ( x(t) )^{p+1}+( y(t) )^{p+1}+(-1)·h(t)·( ( x(t)+y(t) )+(-1)·M(t) )

h(t) = (1/2)·(p+1)·( ( (1+(-1)·k(t))·M(t) )^{p}+( k(t)·M(t) )^{p} )

Teorema:

F(x,y,t) = e^{(p+1)·x(t)}+e^{(p+1)·y(t)}+(-1)·h(t)·( ( e^{x(t)}+e^{y(t)} )+(-1)·M(t) )

h(t) = (1/2)·(p+1)·( ( (1+(-1)·k(t))·M(t) )^{p}+( k(t)·M(t) )^{p} )

Teorema:

F(x,y,t) = x+y+(-1)·h(t)·( (x+y)+(-1)·M(t) )

h(t) = 1

Teorema:

F(x,y,t) = e^{x}+e^{y}+(-1)·h(t)·( (e^{x}+e^{y})+(-1)·M(t) )

h(t) = 1

Teorema:

F(x,y,t) = ( x^{2}+y^{2} )+(-1)·h(t)·( (x+y)+(-1)·M(t) )

h(t) = M(t)

Demostración:

2x+2y = 2·M(t)

Teorema:

F(x,y,t) = ( e^{2x}+e^{2y} )+(-1)·h(t)·( (e^{x}+e^{y})+(-1)·M(t) )

h(t) = M(t)

Teorema:

F(x,y,t) = ( x^{2}+nxy+y^{2} )+(-1)·h(t)·( (x+y)+(-1)·M(t) )

h(t) = (1/2)·(n+2)·M(t)

Demostración:

2x+2y+n·(y+x) = (n+2)·M(t)

Teorema:

F(x,y,t) = ( e^{2x}+ne^{x+y}+e^{2y} )+(-1)·h(t)·( (e^{x}+e^{y})+(-1)·M(t) )

h(t) = (1/2)·(n+2)·M(t)

Ley:

Rezar al Mal matar no tiene sentido,

porque se hace Esparta matando que es vida. 

Rezar al Mal follar con una infiel esclava no tiene sentido,

porque se hace Esparta matando que es vida.