E_{g}(x,y,z) = (-1)·qk·(1/r)^{3}·< x,y,z >
B_{g}(d_{t}[x],d_{t}[y],d_{t}[z]) = qk·(1/r)^{3}·< d_{t}[x],d_{t}[y],d_{t}[z] >
Principio:
E_{g}(yz,zx,xy) = (-1)·qk·(1/r)^{4}·< yz,zx,xy >
B_{g}(d_{t}[yz],d_{t}[zx],d_{t}[xy]) = qk·(1/r)^{4}·< d_{t}[yz],d_{t}[zx],d_{t}[xy] >
Principio:
E_{e}(x,y,z) = qk·(1/r)^{3}·< x,y,z >
B_{e}(d_{t}[x],d_{t}[y],d_{t}[z]) = (-1)·qk·(1/r)^{3}·< d_{t}[x],d_{t}[y],d_{t}[z] >
Principio:
E_{e}(yz,zx,xy) = qk·(1/r)^{4}·< yz,zx,xy >
B_{e}(d_{t}[yz],d_{t}[zx],d_{t}[xy]) = (-1)·qk·(1/r)^{4}·< d_{t}[yz],d_{t}[zx],d_{t}[xy] >
Teorema:
div[ F(x,y,z) ] = d_{xyz}^{3}[ Anti-Potencial[ F(x,y,z) ] ]
Anti-Potencial[ F(x,y,z) ] = int-int-int[ div[ F(x,y,z) ] ]d[x]d[y]d[z]
Teorema:
Anti-div[ F(yz,zx,xy) ] = d_{xyz}^{3}[ Potencial[ F(yz,zx,xy) ] ]
Potencial[ F(yz,zx,xy) ] = int-int-int[ Anti-div[ F(yz,zx,xy) ] ]d[x]d[y]d[z]
Ley:
div[ E_{g}(x,y,z) ] = (-3)·qk·(1/r)^{3}
Anti-Potencial[ E_{g}(x,y,z) ] = (-3)·qk·(1/r)^{3}·xyz
Ley:
div[ int[ B_{g}(d_{t}[x],d_{t}[y],d_{t}[z]) ]d[t] ] = 3qk·(1/r)^{3}
Anti-Potencial[ int[ B_{g}(d_{t}[x],d_{t}[y],d_{t}[z]) ]d[t] ] = 3qk·(1/r)^{3}·xyz
Ley:
Anti-div[ E_{g}(yz,zx,xy) ] = (-3)·qk·(1/r)^{4}
Potencial[ E_{g}(yz,zx,xy) ] = (-3)·qk·(1/r)^{4}·xyz
Ley:
Anti-div[ int[ B_{g}(d_{t}[yz],d_{t}[zx],d_{t}[xy]) ]d[t] ] = 3qk·(1/r)^{4}
Potencial[ int[ B_{g}(d_{t}[yz],d_{t}[zx],d_{t}[xy]) ]d[t] ] = 3qk·(1/r)^{4}·xyz
Ley:
div[ E_{e}(x,y,z) ] = 3qk·(1/r)^{3}
Anti-Potencial[ E_{e}(x,y,z) ] = 3qk·(1/r)^{3}·xyz
Ley:
div[ int[ B_{e}(d_{t}[x],d_{t}[y],d_{t}[z]) ]d[t] ] = (-3)·qk·(1/r)^{3}
Anti-Potencial[ int[ B_{e}(d_{t}[x],d_{t}[y],d_{t}[z]) ]d[t] ] = (-3)·qk·(1/r)^{3}·xyz
Ley:
Anti-div[ E_{e}(yz,zx,xy) ] = 3qk·(1/r)^{4}
Potencial[ E_{e}(yz,zx,xy) ] = 3qk·(1/r)^{4}·xyz
Ley:
Anti-div[ int[ B_{e}(d_{t}[yz],d_{t}[zx],d_{t}[xy]) ]d[t] ] = (-3)·qk·(1/r)^{4}
Potencial[ int[ B_{e}(d_{t}[yz],d_{t}[zx],d_{t}[xy]) ]d[t] ] = (-3)·qk·(1/r)^{4}·xyz
Ley:
m·d_{tt}^{2}[ < x,y,z > ] = p·( E_{e}(x,y,z)+int[ B_{e}(d_{t}[x],d_{t}[y],d_{t}[z]) ]d[t] )
m·d_{tt}^{2}[ < x,y,z > ] = p·( int[ B_{g}(d_{t}[x],d_{t}[y],d_{t}[z]) ]d[t]+E_{g}(x,y,z) )
x(t) = ct·cos(u)·cos(v)
y(t) = ct·sin(u)·cos(v)
z(t) = ct·sin(v)
Ley:
Lap[ E_{e}(x,y,z) ]+(1/c)^{2} [o] 3·d_{tt}^{2}[ int[ B_{e}(d_{t}[x],d_{t}[y],d_{t}[z]) ]d[t] ] = 0
Lap[ int[ B_{g}(d_{t}[x],d_{t}[y],d_{t}[z]) ]d[t] ]+(1/c)^{2} [o] 3·d_{tt}^{2}[ E_{g}(x,y,z) ] = 0
Definición:
Trans[f(x)]-(p) = int[x = 0]-[oo][ f(x)·e^{(-p)·x} ]d[x]
Teorema:
Trans[f(x)+g(x)]-(p) = Trans[f(x)]-(p)+Trans[g(x)]-(p)
Trans[w·f(x)]-(p) = w·Trans[f(x)]-(p)
Teorema:
Trans[cos(x)]-(p) = ( p/(p^{2}+1) )
Trans[sin(x)]-(p) = ( 1/(p^{2}+1) )
Demostración:
(-1)·(1/p)·int[x = 0]-[oo][ cos(x)·(-p)·e^{(-p)·x} ]d[x] = ...
... [x = 0]-[oo]-[ (-1)·(1/p)·cos(x)·e^{(-p)·x} ]+...
.... (-1)·(1/p)·int[x = 0]-[oo][ sin(x)·e^{(-p)·x} ]d[x]
(1/p)^{2}·int[x = 0]-[oo][ sin(x)·(-p)·e^{(-p)·x} ]d[x] = ...
.... [x = 0]-[oo]-[ (1/p)^{2}·sin(x)·e^{(-p)·x} ]+...
... (-1)·(1/p)^{2}·int[x = 0]-[oo][ cos(x)·e^{(-p)·x} ]d[x]
(p^{2}+1)·(1/p)^{2}·int[x = 0]-[oo][ cos(x)·e^{(-p)·x} ]d[x] = (1/p)
(-1)·(1/p)·int[x = 0]-[oo][ sin(x)·(-p)·e^{(-p)·x} ]d[x] = ...
... [x = 0]-[oo]-[ (-1)·(1/p)·sin(x)·e^{(-p)·x} ]+...
.... (1/p)·int[x = 0]-[oo][ cos(x)·e^{(-p)·x} ]d[x]
(-1)·(1/p)^{2}·int[x = 0]-[oo][ cos(x)·(-p)·e^{(-p)·x} ]d[x] = ...
.... [x = 0]-[oo]-[ (-1)·(1/p)^{2}·cos(x)·e^{(-p)·x} ]+...
... (-1)·(1/p)^{2}·int[x = 0]-[oo][ sin(x)·e^{(-p)·x} ]d[x]
(p^{2}+1)·(1/p)^{2}·int[x = 0]-[oo][ sin(x)·e^{(-p)·x} ]d[x] = (1/p)^{2}
Teorema:
Trans[cos(x)]-(p) + Trans[i·sin(x)]-(p) = Trans[e^{ix}]-(p)
Teorema:
Trans[cosh(x)]-(p) = ( p/(p^{2}+(-1)) )
Trans[sinh(x)]-(p) = ( 1/(p^{2}+(-1)) )
Teorema:
Trans[cosh(x)]-(p) + Trans[sinh(x)]-(p) = Trans[e^{x}]-(p)
Teorema:
Trans[( cos(x) )^{2}]-(p) = (-1)·(1/p)
Trans[( sin(x) )^{2}]-(p) = 2·(1/p)
Demostración:
( sin(x)+(-1)^{(1/2)} )^{[o(x)o] 2} [o(x)o] (-1)·(1/p)·e^{(-p)·x}
2·(-1)·cos(x) [o(x)o] sin(x) [o(x)o] (-1)·(1/p)·e^{(-p)·x} = 2·sin(x) [o(x)o] (-1)·(1/p)·e^{(-p)·x}
Teorema:
Trans[( cos(x) )^{2}]-(p) + Trans[( sin(x) )^{2}]-(p) = Trans[1]-(p)
Teorema:
Trans[( cosh(x) )^{2}]-(p) = 2·(1/p)
Trans[( sinh(x) )^{2}]-(p) = (1/p)
Demostración:
2·( sinh(x) ) [o(x)o] cosh(x) [o(x)o] (-1)·(1/p)·e^{(-p)·x} = 2·sinh(x) [o(x)o] (-1)·(1/p)·e^{(-p)·x}
( 1^{(1/2)}+cosh(x)+(-1) )^{[o(x)o] 2} [o(x)o] (-1)·(1/p)·e^{(-p)·x}
Teorema:
Trans[( cosh(x) )^{2}]-(p) + (-1)·Trans[( sinh(x) )^{2}]-(p) = Trans[1]-(p)
Teorema:
Trans[( cos[n](x) )^{n+1}]-(p) = n^{n+1}·( 1+(-1)·(n+1)! )·(1/p)
Trans[( sin[n](x) )^{n+1}]-(p) = (n+1)!·n^{n+1}·(1/p)
Demostración:
( sin[n](x)+n·( 1+(-1)·(n+1)! )^{( 1/(n+1) )} )^{[o(x)o] (n+1)} [o(x)o] (-1)·(1/p)·e^{(-p)·x}
(n+1)!·(-1)·cos[n](x) [o(x)o] n^{n}·(-1)·(1/p)·e^{(-p)·x} = (n+1)!·n^{n+1}·(-1)·(1/p)·e^{(-p)·x}
Teorema:
Trans[( cos[n](x) )^{n+1}]-(p) + Trans[( sin[n](x) )^{n+1}]-(p) = Trans[n^{n+1}]-(p)
Teorema:
Trans[( cosh[n](x) )^{n+1}]-(p) = (n+1)!·n^{n+1}·(1/p)
Trans[( sinh[n](x) )^{n+1}]-(p) = ((n+1)!+(-1))·n^{n+1}·(1/p)
Demostración:
(n+1)!·( sinh[n](x) ) [o(x)o] n^{n}·(-1)·(1/p)·e^{(-p)·x} = (n+1)!·n^{n+1} (-1)·(1/p)·e^{(-p)·x}
( ((n+1)!+(-1))^{( 1/(n+1) )}·n+cosh[n](x)+(-n) )^{[o(x)o] (n+1)} [o(x)o] (-1)·(1/p)·e^{(-p)·x}
Teorema:
Trans[( cosh[n](x) )^{n+1}]-(p) + (-1)·Trans[( sinh[n](x) )^{n+1}]-(p) = Trans[n^{n+1}]-(p)
Teorema:
Si f(0) = 0 ==> Trans[ d_{x}[f(x)] ]-(p) = p·Trans[f(x)]-(p)
Demostración:
Trans[f(x)]-(p) = [x = 0]-[oo][ (-1)·(1/p)·f(x)·e^{(-p)·x} ]+(1/p)·Trans[ d_{x}[f(x)] ]-(p)
Teorema:
Trans[ 1+(-1)·cos(x) ]-(p) = (1/p)·Trans[ sin(x) ]-(p) = (1/p)·( 1/(p^{2}+1) )
Trans[ 1+(-1)·cos(x) ]-(p) = (1/p)+(-1)·( p/(p^{2}+1) ) = (1/p)·( 1/(p^{2}+1))
Trans[ 1+(-1)·cosh(x) ]-(p) = (1/p)·Trans[(-1)·sinh(x)]-(p) = (1/p)·(-1)·( 1/(p^{2}+(-1)) )
Trans[ 1+(-1)·cosh(x) ]-(p) = (1/p)+(-1)·( p/(p^{2}+(-1)) ) = (1/p)·(-1)·( 1/(p^{2}+(-1)) )
Teorema:
Trans[e^{ax}]-(p) = ( 1/(p+(-a)) )
Teorema:
Trans[ ( e^{x}+(-1) )^{2} ]-(p) = (2/p)·( ( 1/(p+(-2)) )+(-1)·( 1/(p+(-1)) ) = ...
... (2/p)·( 1/( (p+(-2))·(p+(-1)) ) )
Trans[ e^{2x}+(-2)·e^{x}+1 ]-(p) = ( 1/(p+(-2)) )+(-1)·( 2/(p+(-1)) )+(1/p) = ...
... ( 1/(p+(-2)) )+(-1)·( (p+1)/(p^{2}+(-p)) ) = (2/p)·( 1/( (p+(-2))·(p+(-1)) ) )
Teorema:
Trans[ e^{x}+(-1) ]-(p) = ( 1/(p+(-1)) )+(-1)·(1/p) = (1/p)·( 1/(p+(-1)) ) = (1/p)·Trans[e^{x}]-(p)
Teorema:
Trans[x^{n}]-(p) = n!·(1/p)^{n+1}
Demostración:
Trans[x^{n+1}]-(p) = (1/p)·Trans[(n+1)·x^{n}]-(p) = (1/p)·(n+1)·n!·(1/p)^{n+1} = (n+1)!·(1/p)^{n+2}
Teorema:
Trans[(1/x)^{n}]-(p) = (1/n!)·(1/p)^{n+1}
Demostración:
[ Trans[ ( x /o(x)o/ x^{n+1} ) ]-(p) = Trans[ ( 1/(n+1)! )·x ]-(p) ] = ...
... (1/p)·( 1/(n+1) )·[ Trans[ ( x /o(x)o/ x^{n} ) ]-(p) = Trans[ (1/n!)·x ]-(p) ] = ...
... (1/p)·( 1/(n+1) )·(1/n!)·(1/p)^{n+1} = ( 1/(n+1)! )·(1/p)^{n+2}
Teorema:
Trans[ax+b]-(p) = a·(1/p)^{2}+b·(1/p)
Trans[ax^{2}+bx+c]-(p) = 2a·(1/p)^{3}+b·(1/p)^{2}+c·(1/p)
Teorema:
Trans[a·(1/x)+b]-(p) = a·(1/p)^{2}+b·(1/p)
Trans[a·(1/x)^{2}+b·(1/x)+c]-(p) = (1/2)·a·(1/p)^{3}+b·(1/p)^{2}+c·(1/p)
Teorema:
Trans[ sin(x)·cos(x) ]-(p) = 1
Trans[ sinh(x)·cosh(x) ]-(p) = (1/2)
Teorema:
Trans[ ( 1+(-1)·cos(x) )^{2} ]-(p) = (2/p)·( ( 1/(p^{2}+1) )+(-1) ) = (-1)·( (2p)/(p^{2}+1) )
Trans[ 1+(-2)·cos(x)+( cos(x) )^{2} ]-(p) = (1/p)+(-1)·( (2p)/(p^{2}+1) )+(-1)·(1/p)
Teorema:
Trans[ ( 1+(-1)·cosh(x) )^{2} ]-(p) = (2/p)·( (-1)·( 1/(p^{2}+(-1)) )+(1/2) ) = ...
... (1/p)·( (p^{2}+(-3))/(p^{2}+(-1)) )
Trans[ 1+(-2)·cosh(x)+( cosh(x) )^{2} ]-(p) = (1/p)+(-1)·( (2p)/(p^{2}+(-1)) )+2·(1/p) = ...
...(1/p)·( (p^{2}+(-3))/(p^{2}+(-1)) )
Teorema:
( g o f ): ...
... [ {a_{1},...,a_{n}} ] ---> ...
... [ {f(a_{1}),...,f(a_{n})} ] ---> ...
... [ {(g o f)(a_{1}),...,(g o f)(a_{n})} ]
S[ {a_{1},...,a_{n}} ]-(x) = sum[k = 1]-[n][ x^{k} ]
Teorema:
( g o f ): ...
... [ {a_{1}},...,{a_{n}} ] ---> ...
... [ {f(a_{1})},...,{f(a_{n})} ] ---> ...
... [ {(g o f)(a_{1})},...,{(g o f)(a_{n})} ]
S[ {a_{1}},...,{a_{n}} ]-(x) = sum[k = 1]-[n][ kx^{k} ]
Teorema
d_{x}[ S[ {a_{1},..,a_{n}} ]-(1) ] = (1/2)·n·(n+3)
Demostración:
d_{x}[ sum[k = 1]-[n][ x^{k}] ] = sum[k = 1]-[n][ kx^{k+(-1)} ] = ...
... sum[k = 1]-[n][ (k+1)·x^{k} ] = sum[k = 1]-[n][ kx^{k} ]+sum[k = 1]-[n][ x^{k} ]
... sum[k = 1]-[n][ k ]+sum[k = 1]-[n][1] = (1/2)·n·(n+1)+n = (1/2)·n·(n+1)+(1/2)·n·2 = (1/2)·n·(n+3)
Teorema:
( g o f ): ...
... [ P( {a_{1},...,a_{n}} ) ] ---> ...
... [ P( {f(a_{1}),...,f(a_{n})} ) ] ---> ...
... [ P( {(g o f)(a_{1}),...,(g o f)(a_{n})} ) ]
S[ P( {a_{1},..,a_{n}} ) ]-(x) = 1+sum[k = 1]-[n][ [ n // k ]·x^{k} ] = (1+x)^{n}
Teorema
d_{x}[ S[ P( {a_{1},..,a_{n}} ) ]-(1) ] = n·2^{n+(-1)}
Demostración:
d_{x}[ 1+sum[k = 1]-[n][ [ n // k ]·x^{k} ] ] = n·sum[k = 1]-[n][ [ n+(-1) // k+(-1) ]·x^{k+(-1)} ] ...
... n·sum[k = 1]-[n][ [ n+(-1) // k+(-1) ] ] = n·2^{n+(-1)}
Teorema:
( g o f ): ...
... [ < m_{1},...,m_{n} > ] ---> ...
... [ < f(m_{1}),...,f(m_{n}) > ] ---> ...
... [ < (g o f)(m_{1}),...,(g o f)(m_{n}) > ) ]
S[ < m_{1},...,m_{n} > ]-(x) = sum[k = 1]-[n][ k!·x^{k} ]
Teorema
d_{x}[ S[ < m_{1},...,m_{n} > ]-(1) ] = (n+2)!+(-2)
Demostración:
d_{x}[ sum[k = 1]-[n][ k!·x^{k} ] ] = sum[k = 1]-[n][ k·k!·x^{k+(-1)} ] = ...
... sum[k = 1]-[n][ (k+1)·(k+1)!·x^{k} ]
... sum[k = 1]-[n][ (k+1)·(k+1)! ] = (n+2)!+(-2)
Teorema:
( g o f ): ...
... [ { mk,...,mk+(m+(-1)) } ] ---> ...
... [ { f(mk),...,f(mk+(m+(-1))) } ] ---> ...
... [ { (g o f)(mk),...,(g o f)(mk+(m+(-1))) } ) ]
S[ { mk,...,mk+(m+(-1)) } ]-(x) = sum[k = 1]-[n][ [ n // k & j_{1} & ... & j_{m+(-1)} ]·x^{k} ]
Teorema
d_{x}[ S[ { mk,...,mk+(m+(-1)) } ]-(1) ] = n·m^{n+(-1)}
Demostración:
d_{x}[ sum[k = 1]-[n][ [ n // k & j_{1} & ... & j_{m+(-1)} ]·x^{k} ] ] = ...
... n·sum[k = 1]-[n][ [ n+(-1) // k+(-1) & j_{1}+(-1) & ... & j_{m+(-1)}+(-1) ]·x^{k+(-1)} ] = ...
... n·sum[k = 1]-[n][ [ n+(-1) // k+(-1) & j_{1}+(-1) & ... & j_{m+(-1)}+(-1) ] ] = n·m^{n+(-1)}
Lema: [ de los rollos de papel ]
F(r) = 2pi·r+(-h)·pi·r^{2}
h = (1/r)
G(r) = pi·r
Lema: [ de las bolas ]
F(r) = 4pi·r^{2}+(-h)·(4/3)·pi·r^{3}
h = (2/r)
G(r) = (4/3)·pi·r^{2}
Lema: [ del loche ]
F(x,y,z) = 4z+xy+2yz+(-h)·(xyz+(-1)·abc)
h = ( 1/(3abc) )·(4c+2ab+4bc)
Lema: [ del sofá ]
F(x,y,z) = 4z+xy+2yz+zx+(-h)·(xyz+(-1)·abc)
h = ( 1/(3abc) )·(4c+2ab+4bc+2ca)
Lema: [ de la tabla ]
F(x,y,z) = 4z+yx+(-h)·(xyz+(-1)·abc)
h = ( 1/(3abc) )·(4c+2ba)
Lema: [ de la silla ]
F(x,y,z) = 4z+yx+xz+(-h)·(xyz+(-1)·abc)
h = ( 1/(3abc) )·(4c+2ba+2ac)
Ley:
Los matemáticos,
emitimos energía,
pero no sabemos conducir,
y no detectamos ninguna máquina.
Los no matemáticos,
no emiten energía,
pero saben conducir,
y detectan alguna máquina.
Ley:
Los matemáticos,
somos señores,
siendo jueces o generales,
porque emitimos constructor o destructor,
y no puede ninguien parar-nos.
Los no matemáticos,
no son señores,
no siendo jueces ni generales,
porque no emiten constructor ni destructor,
y puede alguien parar-los.
Anexo:
Los matemáticos son señores por el Rey de España:
es juez siendo árbitro de la democracia.
es general siendo comandante en jefe.
Ley:
Que la gente no es,
lo dicen los señores de los hombres.
Que la gente es,
lo dicen los no señores de los hombres.
Ley:
Como te vas a creer a un infiel,
no matemático,
de que soy homosexual,
él sabiendo conducir,
y no ser un señor.
Como no te vas a creer a un fiel,
matemático,
de que soy heterosexual,
él no sabiendo conducir,
y ser un señor.
Teorema:
Trans[sin(ax)]-(p) = ( a/(p^{2}+a^{2}) )
Trans[cos(ax)]-(p) = ( p/(p^{2}+a^{2}) )
Demostración:
sin(ax) = (1/2i)·( e^{aix}+(-1)·e^{(-a)·ix} )
Trans[sin(ax)]-(p) = (1/2i)·( ( 1/(p+(-a)·i) )+(-1)·( 1/(p+ai) ) )
Teorema:
Trans[e^{(-c)·x}·f(x)]-(p) = Trans[f(x)]-(p+c)
Teorema:
Trans[f(x)]-(p) = ( 1/(p^{2}+8p+41) ) <==> f(x) = (1/5)·e^{(-4)·x}·sin(5x)
Trans[ d_{x}[f(x)] ]-(p) = ( p/(p^{2}+8p+41) ) <==> ...
... d_{x}[f(x)] = e^{(-4)·x}·( cos(5x)+(-1)·(4/5)·sin(5x) )
Teorema:
Trans[f(x)]-(p) = ( 1/(p^{2}+4p+13) ) <==> f(x) = (1/3)·e^{(-2)·x}·sin(3x)
Trans[ d_{x}[f(x)] ]-(p) = ( p/(p^{2}+4p+13) ) <==> ...
... d_{x}[f(x)] = e^{(-2)·x}·( cos(3x)+(-1)·(2/3)·sin(3x) )
Teorema:
Trans[f(x)]-(p) = ( 1/(p+a) ) <==> f(x) = e^{(-a)·x}·( sinh(x) )^{2}
Trans[ d_{x}[f(x)] ]-(p) = ( p/(p+a) ) <==> ...
... d_{x}[f(x)] = e^{(-a)·x}·( 2·sinh(x)·cosh(x)+(-a)·( sinh(x) )^{2} )
Demostración:
Trans[e^{(-a)·x}·2·sinh(x)·cosh(x)]-(p) = (p+a)^{0} = 1
Teorema:
Trans[f(x)]-(p) = ( p^{2}/(p^{2}+(a+b)·p+ab) ) = ...
... ( (ab)/(a+(-b)) )·( (1/b)·( p/(p+a) )+(-1)·(1/a)·( p/(p+b) ) ) <==> ...
... f(x) = ( (ab)/(a+(-b)) )·( ...
... (1/b)·e^{(-a)·x}·( 2·sinh(x)·cosh(x)+(-a)·( sinh(x) )^{2} )+...
... (-1)·(1/a)·e^{(-b)·x}·( 2·sinh(x)·cosh(x)+(-b)·( sinh(x) )^{2} ) )
Teorema:
Trans[f(x)]-(p) = ( p^{2}/(p^{2}+3p+2) ) = 2·( ( p/(p+2) )+(-1)·(1/2)·( p/(p+1) ) ) <==> ...
... f(x) = 2e^{(-2)·x}·( 2·sinh(x)·cosh(x)+(-2)·( sinh(x) )^{2} )+...
... (-1)·e^{(-1)·x}·( 2·sinh(x)·cosh(x)+(-1)·( sinh(x) )^{2} )
Teorema:
Trans[f(x)]-(p) = ( 1/(p+a)^{n+1} ) <==> f(x) = e^{(-a)·x}·(1/n!)·x^{n}
Trans[ d_{x}[f(x)] ]-(p) = ( p/(p+a)^{n+1} ) = (-a)·( 1/(p+a)^{n+1} )+( 1/(p+a)^{n} ) <==> ...
... d_{x}[f(x)] = (-a)·e^{(-a)·x}·(1/n!)·x^{n}+e^{(-a)·x}·( 1/(n+(-1))! )·x^{n+(-1)}
Teorema:
Trans[f(x)]-(p) = ( 1/(p+a)^{2} ) <==>f(x) = e^{(-a)·x}·x
Trans[ d_{x}[f(x)] ]-(p) = ( p/(p+a)^{2} ) = (-a)·( 1/(p+a)^{2} )+( 1/(p+a) ) <==> ...
... d_{x}[f(x)] = (-a)·e^{(-a)·x}·x+e^{(-a)·x}
Lema:
Sea n >] 1 ==>
( y(x) )^{n}·d_{x}[y(x)] = 1 >] x >] 0
y(x) = ( (n+1)·x )^{( 1/(n+1) )}
w(x) = ( y(x) )^{n+1}
Socialismo:
1 >] ( 2/(n+1) ) >] 0
w( 2/(n+1) ) = 2€
Social-Democracia:
1 >] ( 1/(n+1) ) >] 0
w( 1/(n+1) ) = 1€
Lema:
Sea n >] 1 ==>
e^{(n+1)·y(x)}·d_{x}[y(x)] = 1 >] x >] 0
y(x) = ( 1/(n+1) )·ln( (n+1)·x )
w(x) = e^{(n+1)·y(x)}
Socialismo:
1 >] ( 2/(n+1) ) >] 0
w( 2/(n+1) ) = 2€
Social-Democracia:
1 >] ( 1/(n+1) ) >] 0
w( 1/(n+1) ) = 1€
Teorema: [ de área de un sector circular ]
A(r) = (1/2)·wr^{2}
int[x = 0]-[r][y = 0]-[r][ pi ]d[x]d[y] = pi·r^{2}
4·int[s = (-1)·(pi/4)]-[(pi/4)][ (1/2)·pi·r·cos(2s) ]d[r]d[s] = pi·r^{2}
Teorema: [ de superficie de un sector esférico ]
S(r) = 2wr^{2}
int[x = 0]-[r][y = 0]-[r][ 4pi ]d[x]d[y] = 4pi·r^{2}
4·int[s = (-1)·(pi/4)]-[(pi/4)][ (1/2)·4pi·r·cos(2s) ]d[r]d[s] = 4pi·r^{2}
Ley:
No se puede creer que un infiel es un señor.
El esclavo no es mayor que su señor,
ni el enviado mayor que el que lo envía.
Ley:
No se puede poner un infiel por encima de un fiel.
El esclavo no es mayor que el enviado.
Ley:
No se puede joder a un fiel que estudia.
El señor no es mayor que el que lo envía.
Ley:
No se puede aplicar sexo estudiando,
porque el esclavo no es mayor que el que te envía.
No se puede aplicar violencia estudiando,
porque el esclavo no es mayor que el que te envía.
Anexo:
Han rezado pinchar-me con Xeplion y Risperidona,
haciende el esclavo mayor que el que lo envía porque estudio.
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