∫ [ ( ln(x) )^{n} ] d[x] = (1/(n+1))·( ln(x) )^{n+1} [o(x)o] (1/2)·x^{2}
∫ [ ( ln( f(x) ) )^{n} ] d[x] = ...
... (1/(n+1))·( ln( f(x) ) )^{n+1} [o(x)o] ∫ [ f(x) ] d[x] [o(x)o] ( f(x) )^{[o(x)o](-1)}
∫ [ ( ln( ax^{2}+bx ) )^{n} ] d[x] = ...
... (1/(n+1))·( ln( ax^{2}+bx ) )^{n+1} [o(x)o] ( a·(1/3)·x^{3}+b·(1/2)·x^{2} ) [o(x)o] (1/2a)·ln( 2ax+b )
sábado, 22 de febrero de 2020
jueves, 20 de febrero de 2020
psíquica depresión
depresión para-noide: de nodo o centro.
desactivación del centro del campo de proyección de objetivos
no salir de casa
no ducharse
no cocinar
desactivación del centro del campo de proyección de objetivos
no salir de casa
no ducharse
no cocinar
psíquica esquizofrenia
esquizofrenia para-noide: de nodo, centro o chakra.
activación de centros de ondas.
alucinación de imágenes.
alucinación de sonidos.
activación de centros de ondas.
alucinación de imágenes.
alucinación de sonidos.
domingo, 16 de febrero de 2020
series numériques criteri
teorema:
Si [∀k][ k€N ==> [∃s][ s > 0 & a_{k} [< s^{k} < 1 & (a_{k}/a_{k+1}) [< a_{k+(-1)} ] ] ==> ...
... ∑ a_{k} [< ( 1/( 1+(-1)·s^{2} ) ) [< oo
demostració:
(a_{k}/a_{k+1}) [< a_{k+(-1)}
a_{k} [< a_{k+1}a_{k+(-1)} [< s^{k+1}s^{k+(-1)} = s^{2k}
∑ a_{k} [< ∑ s^{2k} [< ( 1/( 1+(-1)·s^{2} ) ) [< oo
teorema:
Si [∀k][ k€N ==> [∃s][ s > 0 & a_{k} [< s^{k} < 1 & (a_{k}/a_{k+p}) [< a_{k+(-p)} ] ] ==> ...
... ∑ a_{k} [< ( 1/( 1+(-1)·s^{2} ) ) [< oo
Si [∀k][ k€N ==> [∃s][ s > 0 & a_{k} [< s^{k} < 1 & (a_{k}/a_{k+1}) [< a_{k+(-1)} ] ] ==> ...
... ∑ a_{k} [< ( 1/( 1+(-1)·s^{2} ) ) [< oo
demostració:
(a_{k}/a_{k+1}) [< a_{k+(-1)}
a_{k} [< a_{k+1}a_{k+(-1)} [< s^{k+1}s^{k+(-1)} = s^{2k}
∑ a_{k} [< ∑ s^{2k} [< ( 1/( 1+(-1)·s^{2} ) ) [< oo
teorema:
Si [∀k][ k€N ==> [∃s][ s > 0 & a_{k} [< s^{k} < 1 & (a_{k}/a_{k+p}) [< a_{k+(-p)} ] ] ==> ...
... ∑ a_{k} [< ( 1/( 1+(-1)·s^{2} ) ) [< oo
series numériques criteri del quocient
teorema:
Si [∀k][ k€N ==> [∃s][ s > 0 & a_{1} [< 1 & ( a_{k+1}/a_{k} ) [< s [< ( 1+(-1)(1/oo) ) ] ] ==> ...
... ∑ a_{k} [< oo
demostració:
( a_{k+1}/a_{k} ) [< s
a_{k+1} [< s·a_{k}
a_{k+1} [< s^{k+1}
∑ a_{k} [< ∑ s^{k} [< ( 1/(1+(-s)) ) [< oo
teorema:
( k/(k+1) ) = ( 1+( (-1)/(k+1) ) ) [< ( 1+(-1)(1/oo) ) = s
∑ ( 1/k ) [< oo
series numériques criteri de la arrel enéssima
teorema:
Si [∀k][ k€N ==> [∃s][ s > 0 & ( a_{k} )^{(1/k)} [< s [< ( 1+(-1)(1/oo) ) ] ] ==> ∑ a_{k} [< oo
demostració:
∑ a_{k} [< ∑ s^{k} [< ( 1/(1+(-s)) ) [< oo
Si [∀k][ k€N ==> [∃s][ s > 0 & ( a_{k} )^{(1/k)} [< s [< ( 1+(-1)(1/oo) ) ] ] ==> ∑ a_{k} [< oo
demostració:
∑ a_{k} [< ∑ s^{k} [< ( 1/(1+(-s)) ) [< oo
analisis funcional formes integrals
∫ [0-->1]-[ ( (-1)·( k/a )·x+( (2k)/b ) ) [o] (ax+b) ] d[x] = k
∫ [0-->1]-[ ( (-1)·( k/a )·e^{x}+( k/b )·e^{2} ) [o] (a·e^{x}+b) ] d[x] = k
∫ [0-->1]-[ ( ( (12k)/(7a) )·( 1/(x+1)^{2} )+( k/b )·( 1/(x+1) ) ) [o] ...
... ( a·( 1/(x+1)^{2} )+b·( 1/(x+1) ) ) ] d[x] = k
∫ [0-->1]-[ ( (-1)·( k/a )·e^{x}+( k/b )·e^{2} ) [o] (a·e^{x}+b) ] d[x] = k
∫ [0-->1]-[ ( ( (12k)/(7a) )·( 1/(x+1)^{2} )+( k/b )·( 1/(x+1) ) ) [o] ...
... ( a·( 1/(x+1)^{2} )+b·( 1/(x+1) ) ) ] d[x] = k
operadors ortogonals autoadjunts
F(P(x)) [o] G(P(x)) = 0
(-1)·F(P(x)) [o] G(P(x)) = 0
F(P(x)) [o] (-1)·G(P(x)) = 0
(-1)·F(P(x)) [o] (-1)·G(P(x)) = 0
F(a·e^{2x}+b·e^{x}) = 2a·e^{2x}+b·e^{x}
G(a·e^{2x}+b·e^{x}) = (-1)( 1/(2a) )·e^{2x}+(1/b)·e^{x}
operadors ortogonals autoadjunts
F(P(x)) [o] G(P(x)) = 0
(-1)·F(P(x)) [o] G(P(x)) = 0
F(P(x)) [o] (-1)·G(P(x)) = 0
(-1)·F(P(x)) [o] (-1)·G(P(x)) = 0
F(ax^{2}+bx) = 2ax+b
G(ax^{2}+bx) = (-1)( 1/(2a) )·x+(1/b)
F(ax^{3}+bx^{2}+cx) = 3ax^{2}+2bx+c
G(ax^{3}+bx^{2}+cx) = (-1)( 1/(3a) )·x^{2}+(-1)( 1/(2b) )·x+(2/c)
F(ax^{2}+bx+c) = (a/3)x^{3}+(b/2)x^{2}+cx
G(ax^{2}+bx+c) = (-1)( 3/a )·x^{3}+(-1)( 2/b )·x^{2}+(2/c)·x
(-1)·F(P(x)) [o] G(P(x)) = 0
F(P(x)) [o] (-1)·G(P(x)) = 0
(-1)·F(P(x)) [o] (-1)·G(P(x)) = 0
F(ax^{2}+bx) = 2ax+b
G(ax^{2}+bx) = (-1)( 1/(2a) )·x+(1/b)
F(ax^{3}+bx^{2}+cx) = 3ax^{2}+2bx+c
G(ax^{3}+bx^{2}+cx) = (-1)( 1/(3a) )·x^{2}+(-1)( 1/(2b) )·x+(2/c)
F(ax^{2}+bx+c) = (a/3)x^{3}+(b/2)x^{2}+cx
G(ax^{2}+bx+c) = (-1)( 3/a )·x^{3}+(-1)( 2/b )·x^{2}+(2/c)·x
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