formulario de calculo
DESCRIPTION
KTRANSCRIPT
-
LICONALICONALICONAPRESIDENTE
REGIONALPRESIDENTE
REGIONAL
FORMULARIO DE CLCULODIFERENCIAL E INTEGRALFORMULARIO DE CLCULODIFERENCIAL E INTEGRAL
Un Gran Saludo atodos los Estudiantes
Un Gran Saludo atodos los Estudiantes
-
FORMULARIO DE
CLCULO DIFERENCIAL E
INTEGRAL
VALOR ABSOLUTO
1 1
1 1
si 0 si 0
y
0 y 0 0
n n
k kk k
n n
k kk k
a aa
a aa a
a a a a
a a a
ab a b a a
a b a b a a
= =
= =
=
-
( ) ( ) ( ) ( ) ( )( )( ) ( )( )
( ) ( ) ( ) ( )( ) ( )
( ) ( )
20 0
0 0 0
0 0
2
2 3
3 5 7 2 11
'''
2!
: Taylor!
'' 00 ' 0
2!0
: Maclaurin!
12! 3! !
sen 13! 5! 7! 2 1 !
cos
nn
n n
nx
nn
f x x xf x f x f x x x
f x x xn
f xf x f f x
f xn
x x xe xn
x x x xx xn
x
= + ++ +
= + +
+ +
= + + + + + +
= + + + =
ALGUNAS SERIES
"
"
" "
"
( ) ( )( ) ( )
( )
2 4 6 2 21
2 3 41
3 5 7 2 11
1 12! 4! 6! 2 2 !
ln 1 12 3 4
tg 13 5 7 2 1
nn
nn
nn
x x x xn
x x x xx xn
x x x xx xn
+ + + + = + + +
= + + +
"
"
"
( )( )
2 2
2 2
sen cossen
cos sencos
auau
auau
e a bu b bue bu du
a be a bu b bu
e bu dua b
= ++= +
MAS INTEGRALES
( )
( )
2 2
2 2
2 2
2 2 2 2
2 2
22 2 2 2
22 2 2 2 2 2
sen
cos
ln
1 ln
1 cos
1 sec
sen2 2
ln2 2
du uaa uua
du u u au a
du uau a u a a u
du aa uu u a
ua au a ua u du a u
au au a du u a u u a
= =
= +
= + =
=
= +
= +
INTEGRALES CON RAZ CUADRADA
( )( )
2 2
2 22 2
2 22 2
1 tg
1 ctg
1 ln 21 ln
2
du ua au a
ua a
du u a u aa u au a
du a u u aa a ua u
= +=
= >++=
=
=
= +
DERIVADA DE FUNCS LOG&EXP
( )( )( )( )( )( )( )
2
2
sen cos
cos sen
tg sec
ctg csc
sec sec tg
csc csc ctg
vers sen
d duu udx dxd duu udx dxd duu udx dxd duu udx dxd duu u udx dxd duu u udx dxd duu udx dx
=
=
=
=
=
=
=
DERIVADA DE FUNCIONES TRIG.
( )( )( )( )( )( )(
)
2
2
2
2
2
2
1sen1
1cos1
1tg1
1ctg1
si 11sec si 11 si 11csc si 11
1vers2
d duudx dxud duudx dxud duudx dxud duudx dxu
ud duuudx dxu uud duuudx dxu u
d udx u u
=
= = + = +
+ > = < > = + <
=
DERIV. DE FUNCIONES TRIG. INVERSAS
2
dudx
2
2
senh cosh
cosh senh
tgh sech
ctgh csch
sech sech tgh
csch csch ctgh
d duu udx dxd duu udx dxd duu udx dxd duu udx dxd duu u udx dxd duu u udx dx
=
=
=
=
=
=
DERIVADA DE FUNCIONES HIPERBLICAS
1
2
-11
-12
12
12
11
2
1senh1
si cosh 01cosh , 1 si cosh 01
1tgh , 11
1ctgh , 11
si sech 0, 0,1sech1
d duudx dxu
ud duu udx dx uud duu udx dxud duu udx dxu
u ud duudx dxu u
= ++ > = > =
DERIVADA DE FUNCIONES HIP INVERSAS
1
1
2
1
si sech 0,0,1
1csch , 01
u u
d duu udx dxu u
+ < = +
( )( )
( ) ( )( )
( )
2
2
01ln
1ln ln
1
ln ln ln 1
1log ln ln 1ln ln
log 2log 14
ln 2ln 14
u u
uu
uu
u u
a
a a
e du e
aaa duaa
aua du ua a
ue du e u
udu u u u u u
uudu u u u ua auu udu u
uu udu u
=>= =
= = = = =
=
=
INTEGRALES DE FUNCS LOG & EXP
( ) ( ){ } ( ) ( )( ) ( )( ) ( ) ( )( ) ( )( )( ) ( ) ( )
( ) [ ]( ) ( )( ) ( )
0
, , ,
,
b b b
a a ab b
a ab c b
a a cb a
a ba
ab
a
b b
a a
f x g x dx f x dx g x dx
cf x dx c f x dx c
f x dx f x dx f x dx
f x dx f x dx
f x dx
m b a f x dx M b a
m f x M x a b m M
f x dx g x dx
f x g x x a
= = = += =
INTEGRALES DEFINIDAS, PROPIEDADES
\
\
[ ]( ) ( ) si b b
a a
b
f x dx f x dx a b