Formulario Calculo Diferencia E Integral
Fórmulas de Cálculo Diferencial e Integral (Página 1 de 3)
Fórmulas de
Cálculo Diferencial
e Integral VER.6.8
Jesús Rubí Miranda (jesusrubim@yahoo.com)
http://www.geocities.com/calculusjrm/
VALOR ABSOLUTO
( 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
( a + b ) ⋅ ( a 5 − a 4 b + a 3 b 2 − a 2 b 3 + ab 4 − b 5 ) = a 6 − b 6
⎛n
⎞
k +1
( a + b ) ⋅ ⎜ ∑ ( −1) a n− k b k −1 ⎟ = a n + b n ∀ n ∈
⎝ k =1
⎠
⎛
⎞
a n − k b k −1 ⎟ = a n − b n ∀ n ∈
⎝ k =1
⎠
SUMAS Y PRODUCTOS
a = −a
a1 + a2 +
a ≤ a y −a ≤ a
a ≥0 y a =0 ⇔ a=0
ab = a b ó
n
a+b ≤ a + b ó
k
n
n
≤ ∑ ak
k
k =1
(a ⋅b)
=a
nk =1
k =1
n
k =1
ap
= a p−q
aq
p
k =1
n
∑(a
k =1
= a ⋅b
p
p
ap
⎛a⎞
⎜⎟=p
b
⎝b⎠
a p/q = a p
q
LOGARITMOS
log a N = x ⇒ a x = N
log a MN = log a M + log a N
M
= log a M − log a N
N
log a N r = r log a N
log a
log b N ln N
=
log a N =
log b a ln a
1+ 3 + 5 +
log10 N = log N y log e N = ln N
ππ
,
22
tg 2 θ + 1 = sec 2 θsin ( −θ ) = − sin θ
sin θ + cos 2 θ = 1
2
1 + ctg 2 θ = csc 2 θ
( a + b) ⋅ ( a − b) = a − b
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 + b33
( a − b ) = a 3 − 3a 2b + 3ab 2 − b3
2
( a + b + c ) = a 2 + b 2 + c 2 + 2ab + 2ac + 2bc
2
( a − b ) ⋅ ( a + ab + b ) = a − b
( 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
2
n
2
⎞
3
3
( a − b ) ⋅ ⎜ ∑ a n − k b k −1 ⎟ = a n − b n
⎝ k =1
⎠
∀n ∈
tg (θ + π ) = tg θ
s en x
co s x
tg x-1 . 5
-2
0
2
4
6
sin (θ + nπ ) = ( −1) sin θ
n
8
Gráfica 2. Las funciones trigonométricas csc x ,
sec x , ctg x :
2. 5
1
0. 5
2
0
-0 . 5
-1
k =1
( x1 + x2 +
+ xk ) = ∑
n
-1 . 5
-2
0
2
4
6
8
xknk
4
n
⎛ 2n + 1 ⎞
sin ⎜
π ⎟ = ( −1)
⎝2
⎠
⎛ 2n + 1 ⎞
cos ⎜
π⎟=0
⎝2
⎠
⎛ 2n + 1 ⎞
tg ⎜
π⎟=∞
⎝2
⎠
cosh :
tgh :
ctgh:
→
→ [1, ∞
→ −1 , 1
− {0} → −∞ , −1 ∪ 1, ∞
sech :
→ 0 ,1]
csch :
− {0} →
-1
ar c s en x
a r c co s x
ar c tg x
-2
-1
0
1
2
3
cos 2θ = cos 2 θ − sin 2 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
− {0}
Gráfica 5. Las funciones hiperbólicas sinh x ,
cosh x , tgh x :5
4
π⎞
⎛
sin θ = cos ⎜ θ − ⎟
2⎠
⎝
π⎞
⎛
cos θ = sin ⎜ θ + ⎟
2⎠
⎝
tg α ± tg β
tg (α ± β ) =
1 ∓ t g α tg β
sin 2θ = 2 sin θ cos θ
0
CO
sinh :
n
3
2
1
0
-1
-2
cos (α ± β ) = cos α cos β ∓ sin α sin β
1
-2
-3
tg (θ + nπ ) = tg θ
sin ( nπ ) = 0
sin (α ± β ) = sin α cos β ± cos α sin β
2
π radianes=180
CA
-4
3
e = 2.71828182846…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
θ
-6
Gráfica 3. Las funciones trigonométricas inversas
arcsin x , arccos x , arctg x :
CONSTANTES
π = 3.14159265359…
HIP
cs c x
se c x
ctg x
-2
n!
n
x1n1 ⋅ x2 2
n1 ! n2 ! nk !
n
tg ( nπ ) = 0
1. 5
-2 . 5
-8
cos (θ + nπ )= ( −1) cos θ
cos ( nπ ) = ( −1)
2
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
e x + e− x
1
=
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 =
cos (θ + π ) = − cos θ
-1
⎛n⎞
n!
, k≤n
⎜ ⎟=
⎝ k ⎠ ( n − k )!k !
n
⎛n⎞
n
( x + y ) = ∑ ⎜ ⎟ xn−k y k
k =0 ⎝ k ⎠...
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