Fórmulas De Cálculo Diferencial E Integral
Páginas: 14 (3251 palabras)
Publicado: 8 de junio de 2012
Fórmulas de Cálculo Diferencial e Integral (Página 1 de 3)
Fórmulas de
Cálculo Diferencial
e Integral ACTUALIZADO AGO-2007
Jesús Rubí Miranda (jesusrubim@yahoo.com)
Móvil. Méx. DF. 044 55 13 78 51 94
⎛
a = −a
a1 + a2 +
a ≤ a y −a ≤ a
a ≥0 y a =0 ⇔ a=0
n
k =1
k
k
k =1
n
(a ⋅b)
=a
p
n
k =1
∑(a
+ a n = ∑ ak
k
= c ∑ ak
= a ⋅b
k =1k =1
− ak −1 ) = an − a0
M
= log a M − log a N
N
r
log a N = r log a N
log b N ln N
=
log a N =
log b a ln a
1+ 3 + 5 +
n
cos (θ + nπ ) = ( −1) cos θ
n
tg (θ + nπ ) = tg θ
( a − b ) ⋅ ( a 2 + ab + b 2 ) = a 3 − b 3
( a − b ) ⋅ ( a 3 + a 2 b + ab 2 + b 3 ) = a 4 − b 4
( a − b ) ⋅ ( a 4 + a 3 b + a 2 b 2 + ab 3 + b 4 ) = a 5 − b 5
cos ( nπ ) = ( −1)
s en x
co sx
tg x
-6
-4
-2
0
2
4
6
n
1
0
6. CONSTANTES
π = 3.14159265359…
e = 2.71828182846…
7. TRIGONOMETRÍA
CO
1
sen θ =
cscθ =
HIP
sen θ
CA
1
cosθ =
secθ =
HIP
cosθ
sen θ CO
1
tgθ =
ctgθ =
=
cosθ CA
tg θ
-1
-1 . 5
cs c x
se c x
ctg x
-2
-2 . 5
-8
-6
-4
-2
0
2
4
6
Gráfica 3. Las funciones trigonométricas inversasarcsin x , arccos x , arctg x :
4
− {0} → −∞ , −1 ∪ 1, ∞
sech :
→ 0 ,1]
csch :
− {0} →
3
2
1
π radianes=180
-1
ar c s en x
a r c co s x
ar c tg x
-2
-1
0
1
2
3
− {0}
Gráfica 5. Las funciones hiperbólicas sinh x ,
cosh x , tgh x :
5
4
3
2
1
0
-1
-2
cos (α ± β ) = cos α cos β ∓ sin α sin β
tg α ± tg β
1 ∓ t g α tg β
sin 2θ = 2sin θ cos θ
tg (α ± β ) =
cos 2θ = cos θ − sin θ
2 tg θ
tg 2θ =
1 − tg 2 θ
1
sin 2 θ = (1 − cos 2θ )
2
1
cos 2 θ = (1 + cos 2θ )
2
1 − cos 2θ
tg 2 θ =
1 + cos 2θ
2
-2
-3
ctgh :
→ [1, ∞
→ −1 , 1
sin (α ± β ) = sin α cos β ± cos α sin β
8
0
∀n ∈
n
⎛ 2n + 1 ⎞
sin ⎜
π ⎟ = ( −1)
⎝2
⎠
⎛ 2n + 1 ⎞
cos ⎜
π⎟=0
⎝2
⎠
→
π⎞
⎛
sin θ = cos ⎜ θ − ⎟
2⎠
⎝π⎞
⎛
cos θ = sin ⎜ θ + ⎟
2⎠
⎝
0. 5
xknk
tgh :
⎛ 2n + 1 ⎞
tg ⎜
π⎟=∞
⎝2
⎠
2
1. 5
n!
n
x1n1 ⋅ x2 2
n1 ! n2 ! nk !
cosh :
n
tg ( nπ ) = 0
8
2. 5
+ xk ) = ∑
sinh :
sin ( nπ ) = 0
-0 . 5
( x1 + x2 +
cos (θ + π ) = − cos θ
tg (θ + π ) = tg θ
Gráfica 2. Las funciones trigonométricas csc x ,
sec x , ctg x :
⎛n⎞
n!
, k≤n
⎜ ⎟=
⎝ k ⎠ ( n − k) !k !
n
⎛n⎞
n
( x + y ) = ∑ ⎜ ⎟ x n −k y k
k =0 ⎝ k ⎠
sin (θ + π ) = − sin θ
sin (θ + nπ ) = ( −1) sin θ
-1 . 5
ex − e− x
2
e x + e− x
cosh x =
2
sinh x e x − e − x
=
tgh x =
cosh x e x + e− x
1
e x + e− x
ctgh x =
=
tgh x e x − e − x
1
2
sech x =
=
cosh x e x + e − x
1
2
csch x =
=
sinh x e x − e − x
sinh x =
tg (θ + 2π ) = tg θ
-1
1
⎡cos (α −β ) + cos (α + β ) ⎤
⎦
2⎣
tg α + tg β
ctg α + ctg β
9. FUNCIONES HIPERBÓLICAS
cos (θ + 2π ) = cos θ
0
1
⎡sin (α − β ) + sin (α + β ) ⎤
⎦
2⎣
1
sin α ⋅ sin β = ⎡cos (α − β ) − cos (α + β ) ⎤
⎦
2⎣
sin α ⋅ cos β =
tg α ⋅ tg β =
tg ( −θ ) = − tg θ
-0 . 5
sin (α ± β )
cos α ⋅ cos β
cos α ⋅ cos β =
sin (θ + 2π ) = sin θ
0. 5
k =1
( a + b ) ⋅ ( a − b ) =a 2 − b2
2
( a + b ) ⋅ ( a + b ) = ( a + b ) = a 2 + 2ab + b 2
2
( a − b ) ⋅ ( a − b ) = ( a − b ) = a 2 − 2ab + b 2
( x + b ) ⋅ ( x + d ) = x 2 + ( b + d ) x + bd
( ax + b ) ⋅ ( cx + d ) = acx 2 + ( ad + bc ) x + bd
( a + b ) ⋅ ( c + d ) = ac + ad + bc + bd
3
( a + b ) = a3 + 3a 2b + 3ab 2 + b3
3
( a − b ) = a 3 − 3a 2b + 3ab 2 − b3
2
( a + b + c ) = a 2 + b 2 + c 2 + 2ab + 2ac + 2bc⎠
y ∈ 0, π
5
8. IDENTIDADES TRIGONOMÉTRICAS
cos ( −θ ) = cos θ
1
+ ( 2n − 1) = n 2
0
sin ( −θ ) = − sin θ
,
22
1. 5
-2
-8
-2
-5
tg 2 θ + 1 = sec 2 θ
2
n! = ∏ k
4. ALGUNOS PRODUCTOS
a ⋅ ( c + d ) = ac + ad
⎞
1
x
tg α ± tg β =
ar c c tg x
ar c s e c x
a r c cs c x
2
ππ
1
1
(α + β ) ⋅ cos (α − β )
2
2
1
1
sin α...
Fórmulas de
Cálculo Diferencial
e Integral ACTUALIZADO AGO-2007
Jesús Rubí Miranda (jesusrubim@yahoo.com)
Móvil. Méx. DF. 044 55 13 78 51 94
⎛
a = −a
a1 + a2 +
a ≤ a y −a ≤ a
a ≥0 y a =0 ⇔ a=0
n
k =1
k
k
k =1
n
(a ⋅b)
=a
p
n
k =1
∑(a
+ a n = ∑ ak
k
= c ∑ ak
= a ⋅b
k =1k =1
− ak −1 ) = an − a0
M
= log a M − log a N
N
r
log a N = r log a N
log b N ln N
=
log a N =
log b a ln a
1+ 3 + 5 +
n
cos (θ + nπ ) = ( −1) cos θ
n
tg (θ + nπ ) = tg θ
( a − b ) ⋅ ( a 2 + ab + b 2 ) = a 3 − b 3
( a − b ) ⋅ ( a 3 + a 2 b + ab 2 + b 3 ) = a 4 − b 4
( a − b ) ⋅ ( a 4 + a 3 b + a 2 b 2 + ab 3 + b 4 ) = a 5 − b 5
cos ( nπ ) = ( −1)
s en x
co sx
tg x
-6
-4
-2
0
2
4
6
n
1
0
6. CONSTANTES
π = 3.14159265359…
e = 2.71828182846…
7. TRIGONOMETRÍA
CO
1
sen θ =
cscθ =
HIP
sen θ
CA
1
cosθ =
secθ =
HIP
cosθ
sen θ CO
1
tgθ =
ctgθ =
=
cosθ CA
tg θ
-1
-1 . 5
cs c x
se c x
ctg x
-2
-2 . 5
-8
-6
-4
-2
0
2
4
6
Gráfica 3. Las funciones trigonométricas inversasarcsin x , arccos x , arctg x :
4
− {0} → −∞ , −1 ∪ 1, ∞
sech :
→ 0 ,1]
csch :
− {0} →
3
2
1
π radianes=180
-1
ar c s en x
a r c co s x
ar c tg x
-2
-1
0
1
2
3
− {0}
Gráfica 5. Las funciones hiperbólicas sinh x ,
cosh x , tgh x :
5
4
3
2
1
0
-1
-2
cos (α ± β ) = cos α cos β ∓ sin α sin β
tg α ± tg β
1 ∓ t g α tg β
sin 2θ = 2sin θ cos θ
tg (α ± β ) =
cos 2θ = cos θ − sin θ
2 tg θ
tg 2θ =
1 − tg 2 θ
1
sin 2 θ = (1 − cos 2θ )
2
1
cos 2 θ = (1 + cos 2θ )
2
1 − cos 2θ
tg 2 θ =
1 + cos 2θ
2
-2
-3
ctgh :
→ [1, ∞
→ −1 , 1
sin (α ± β ) = sin α cos β ± cos α sin β
8
0
∀n ∈
n
⎛ 2n + 1 ⎞
sin ⎜
π ⎟ = ( −1)
⎝2
⎠
⎛ 2n + 1 ⎞
cos ⎜
π⎟=0
⎝2
⎠
→
π⎞
⎛
sin θ = cos ⎜ θ − ⎟
2⎠
⎝π⎞
⎛
cos θ = sin ⎜ θ + ⎟
2⎠
⎝
0. 5
xknk
tgh :
⎛ 2n + 1 ⎞
tg ⎜
π⎟=∞
⎝2
⎠
2
1. 5
n!
n
x1n1 ⋅ x2 2
n1 ! n2 ! nk !
cosh :
n
tg ( nπ ) = 0
8
2. 5
+ xk ) = ∑
sinh :
sin ( nπ ) = 0
-0 . 5
( x1 + x2 +
cos (θ + π ) = − cos θ
tg (θ + π ) = tg θ
Gráfica 2. Las funciones trigonométricas csc x ,
sec x , ctg x :
⎛n⎞
n!
, k≤n
⎜ ⎟=
⎝ k ⎠ ( n − k) !k !
n
⎛n⎞
n
( x + y ) = ∑ ⎜ ⎟ x n −k y k
k =0 ⎝ k ⎠
sin (θ + π ) = − sin θ
sin (θ + nπ ) = ( −1) sin θ
-1 . 5
ex − e− x
2
e x + e− x
cosh x =
2
sinh x e x − e − x
=
tgh x =
cosh x e x + e− x
1
e x + e− x
ctgh x =
=
tgh x e x − e − x
1
2
sech x =
=
cosh x e x + e − x
1
2
csch x =
=
sinh x e x − e − x
sinh x =
tg (θ + 2π ) = tg θ
-1
1
⎡cos (α −β ) + cos (α + β ) ⎤
⎦
2⎣
tg α + tg β
ctg α + ctg β
9. FUNCIONES HIPERBÓLICAS
cos (θ + 2π ) = cos θ
0
1
⎡sin (α − β ) + sin (α + β ) ⎤
⎦
2⎣
1
sin α ⋅ sin β = ⎡cos (α − β ) − cos (α + β ) ⎤
⎦
2⎣
sin α ⋅ cos β =
tg α ⋅ tg β =
tg ( −θ ) = − tg θ
-0 . 5
sin (α ± β )
cos α ⋅ cos β
cos α ⋅ cos β =
sin (θ + 2π ) = sin θ
0. 5
k =1
( a + b ) ⋅ ( a − b ) =a 2 − b2
2
( a + b ) ⋅ ( a + b ) = ( a + b ) = a 2 + 2ab + b 2
2
( a − b ) ⋅ ( a − b ) = ( a − b ) = a 2 − 2ab + b 2
( x + b ) ⋅ ( x + d ) = x 2 + ( b + d ) x + bd
( ax + b ) ⋅ ( cx + d ) = acx 2 + ( ad + bc ) x + bd
( a + b ) ⋅ ( c + d ) = ac + ad + bc + bd
3
( a + b ) = a3 + 3a 2b + 3ab 2 + b3
3
( a − b ) = a 3 − 3a 2b + 3ab 2 − b3
2
( a + b + c ) = a 2 + b 2 + c 2 + 2ab + 2ac + 2bc⎠
y ∈ 0, π
5
8. IDENTIDADES TRIGONOMÉTRICAS
cos ( −θ ) = cos θ
1
+ ( 2n − 1) = n 2
0
sin ( −θ ) = − sin θ
,
22
1. 5
-2
-8
-2
-5
tg 2 θ + 1 = sec 2 θ
2
n! = ∏ k
4. ALGUNOS PRODUCTOS
a ⋅ ( c + d ) = ac + ad
⎞
1
x
tg α ± tg β =
ar c c tg x
ar c s e c x
a r c cs c x
2
ππ
1
1
(α + β ) ⋅ cos (α − β )
2
2
1
1
sin α...
Leer documento completo
Regístrate para leer el documento completo.