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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 …ver más…

5

-2
-8

tg α ± tg β = ar c c tg x ar c s e c x a r c cs c x

-2
-5

1

n! = ∏ k

⎛

y∈ −

Jesús Rubí M.

1
1
(α + β ) ⋅ cos (α − β )
2
2
1
1 sin α − sin β = 2 sin (α − β ) ⋅ cos (α + β )
2
2
1
1 cos α + cos β = 2 cos (α + β ) ⋅ cos (α − β )
2
2
1
1 cos α − cos β = −2 sin (α + β ) ⋅ sin (α − β )
2
2

sin α + sin β = 2 sin

0

1. 5

p

2

-1

n

pq

3

1

2

n
∑ ⎡ a + ( k − 1) d ⎤ = 2 ⎡ 2a + ( n − 1) d ⎤
⎣
⎦
⎣
⎦ k =1 n = (a + l )
2
n
1 − r n a − rl k −1
∑ ar = a 1 − r = 1 − r k =1 n 1
∑ k = 2 ( n2 + n ) k =1 n 1
∑ k 2 = 6 ( 2n3 + 3n2 + n ) k =1 n 1
∑ k 3 = 4 ( n 4 + 2n3 + n 2 ) k =1 n 1
∑ k 4 = 30 ( 6n5 + 15n4 + 10n3 − n ) k =1

4

y ∈ ⎢− , ⎥
⎣ 2 2⎦ y = ∠ cos x y ∈ [ 0, π ]

Gráfica 1. Las funciones trigonométricas: sin x , cos x , tg x :

− ak −1 ) = an − a0

k

y = ∠ sin x

1 y = ∠ sec x = ∠ cos y ∈ [ 0, π ] x 1
⎡ π π⎤ y = ∠ csc x = ∠ sen y ∈ ⎢− , ⎥ x ⎣ 2 2⎦

∑ ( ak + bk ) = ∑ ak +