aqui les dejo un formulario que en lo personal me ha servido mucho..

1. Formulario de Cálculo Diferencial e Integral Jesús Rubí M.
Formulario de ( a + b ) ⋅ ( a 2 − ab + b2 ) = a3 + b3 θ sen cos tg ctg sec csc
Gráfica 4. Las funciones trigonométricas inversas
arcctg x , arcsec x , arccsc x : sen α + sen β
1 1
= 2sen (α + β ) ⋅ cos (α − β )
( a + b ) ⋅ ( a3 − a 2 b + ab2 − b3 ) = a 4 − b4 0 0 ∞ ∞ 0 2 2
Cálculo Diferencial
1 1
1 1
30 12 3 2 3 2 sen α − sen β = 2 sen (α − β ) ⋅ cos (α + β )
4
3 2 1 3
( a + b ) ⋅ ( a 4 − a3b + a 2 b2 − ab3 + b4 ) = a5 + b5
e Integral VER.4.3 45 1 2 1 2 1 1 2 2 3
2 2
( a + b ) ⋅ ( a5 − a 4 b + a3b2 − a 2 b3 + ab4 − b5 ) = a 6 − b6
1 1
60 3 2 12 3 1 3 2 2 3 cos α + cos β = 2 cos (α + β ) ⋅ cos (α − β )
Jesús Rubí Miranda (jesusrubim@yahoo.com) 2 2 2
90 1 0 ∞ 0 ∞ 1
http://mx.geocities.com/estadisticapapers/ ⎛ n ⎞ cos α − cos β
1 1
= −2sen (α + β ) ⋅ sen (α − β )
( a + b ) ⋅ ⎜ ∑ ( −1) a n− k b k −1 ⎟ = a n + b n ∀ n ∈
k +1
impar ⎡ π π⎤ 1
http://mx.geocities.com/dicalculus/ ⎝ k =1 ⎠ y = ∠ sen x y ∈ ⎢− , ⎥ 2 2
⎣ 2 2⎦
sen (α ± β )
0
VALOR ABSOLUTO ⎛ n
⎞
( a + b ) ⋅ ⎜ ∑ ( −1) y ∈ [ 0, π ]
k +1
a n − k b k −1 ⎟ = a n − b n ∀ n ∈ par y = ∠ cos x tg α ± tg β =
⎧a si a ≥ 0 ⎝ k =1 ⎠
-1
cos α ⋅ cos β
a =⎨
arc ctg x
π π arc sec x
⎩− a si a < 0 y = ∠ tg x y∈ − arc csc x
SUMAS Y PRODUCTOS , 1
⎡sen (α − β ) + sen (α + β ) ⎤
-2
2 2 -5 0 5
sen α ⋅ cos β =
a = −a n
2⎣ ⎦
a1 + a2 + + an = ∑ ak 1 IDENTIDADES TRIGONOMÉTRICAS
a ≤ a y −a≤ a y = ∠ ctg x = ∠ tg y ∈ 0, π 1
k =1
x sen α ⋅ sen β = ⎡cos (α − β ) − cos (α + β ) ⎤
sen θ + cos2 θ = 1 2⎣ ⎦
2
n
a ≥0y a =0 ⇔ a=0
∑ c = nc y = ∠ sec x = ∠ cos
1
y ∈ [ 0, π ] 1 + ctg 2 θ = csc2 θ 1
k =1 cos α ⋅ cos β = ⎡cos (α − β ) + cos (α + β ) ⎤
2⎣ ⎦
n n x
ab = a b ó ∏a = ∏ ak n n
⎡ π π⎤ tg 2 θ + 1 = sec2 θ
∑ ca = c ∑ ak 1
k
k =1 k =1 k y = ∠ csc x = ∠ sen y ∈ ⎢− , ⎥ tg α + tg β
n n k =1 k =1 x ⎣ 2 2⎦ sen ( −θ ) = − sen θ tg α ⋅ tg β =
a+b ≤ a + b ó ∑a ≤ ∑ ak n n n ctg α + ctg β
k =1
k
k =1 ∑(a
k =1
k + bk ) = ∑ ak + ∑ bk
k =1 k =1
Gráfica 1. Las funciones trigonométricas: sen x , cos ( −θ ) = cosθ FUNCIONES HIPERBÓLICAS
cos x , tg x :
EXPONENTES n tg ( −θ ) = − tg θ e x − e− x
a p ⋅ a q = a p+q ∑(a − ak −1 ) = an − a0 senh x =
sen (θ + 2π ) = sen θ
k 2
k =1
2
ap 1.5
e x + e− x
= a p−q n
n cos (θ + 2π ) = cosθ cosh x =
aq ∑ ⎡ a + ( k − 1) d ⎤ = 2 ⎡ 2a + ( n − 1) d ⎤
⎣ ⎦ ⎣ ⎦
1
2
k =1 tg (θ + 2π ) = tg θ
( a p ) = a pq senh x e x − e − x
q 0.5
n tgh x = =
(a + l )
= 0 sen (θ + π ) = − sen θ cosh x e x + e − x
(a ⋅ b) = ap ⋅bp
p
2 -0.5
cos (θ + π ) = − cosθ 1 e x + e− x
n
1 − r n a − rl ctgh x = =
⎛a⎞ ap
p
∑ ar k −1
=a = -1
tg (θ + π ) = tg θ tgh x e x − e − x
⎜ ⎟ = p k =1 1− r 1− r
⎝b⎠
sen x
b -1.5
1 2
sen (θ + nπ ) = ( −1) sen θ sech x = =
cos x n
( n + n)
n
1 2
∑k =
tg x
a p/q
= a
q p -2
-8 -6 -4 -2 0 2 4 6 8 cosh x e x + e − x
2
k =1
cos (θ + nπ ) = ( −1) cos θ
n
1 2
LOGARITMOS csch x = =
∑ k 2 = 6 ( 2n3 + 3n2 + n )
n
1 Gráfica 2. Las funciones trigonométricas csc x ,
log a N = x ⇒ a x = N tg (θ + nπ ) = tg θ senh x e x − e − x
k =1 sec x , ctg x :
log a MN = log a M + log a N senh : →
sen ( nπ ) = 0
∑ k 3 = 4 ( n 4 + 2n3 + n 2 )
n
1
M
2.5
cosh : → [1, ∞
= log a M − log a N cos ( nπ ) = ( −1)
n
log a k =1 2
N tgh : → −1,1
∑ k 4 = 30 ( 6n5 + 15n4 + 10n3 − n )
n
1
tg ( nπ ) = 0
1.5
log a N r = r log a N 1
ctgh : − {0} → −∞ , −1 ∪ 1, ∞
k =1
⎛ 2n + 1 ⎞
+ ( 2n − 1) = n 2 π ⎟ = ( −1) → 0,1]
0.5 n
log b N ln N 1+ 3 + 5 + sen ⎜
log a N = = sech :
⎝ 2 ⎠
0
log b a ln a n
− {0} → − {0}
n! = ∏ k
-0.5
csch :
log10 N = log N y log e N = ln N ⎛ 2n + 1 ⎞
k =1
-1
cos ⎜ π⎟=0
ALGUNOS PRODUCTOS -1.5 ⎝ 2 ⎠ Gráfica 5. Las funciones hiperbólicas senh x ,
⎛n⎞ n! csc x
a ⋅ ( c + d ) = ac + ad ⎜ ⎟= , k≤n -2 sec x
⎛ 2n + 1 ⎞ cosh x , tgh x :
⎝ k ⎠ ( n − k )!k !
ctg x
tg ⎜ π⎟=∞
⎝ 2 ⎠
-2.5
( a + b) ⋅ ( a − b) = a − b
-8 -6 -4 -2 0 2 4 6 8
2 2
5
n
⎛n⎞
( x + y ) = ∑ ⎜ ⎟ xn−k y k π⎞
n
Gráfica 3. Las funciones trigonométricas inversas ⎛
( a + b ) ⋅ ( a + b ) = ( a + b ) = a 2 + 2ab + b2
4
sen θ = cos ⎜θ − ⎟
2
k =0 ⎝ k ⎠ arcsen x , arccos x , arctg x : ⎝ 2⎠ 3
( a − b ) ⋅ ( a − b ) = ( a − b ) = a 2 − 2ab + b 2
2 2
( x1 + x2 + + xk )
n
=∑
n!
x1n1 ⋅ x2 2 ⎛ π⎞
cosθ = sen ⎜θ + ⎟
n nk
x 4
( x + b ) ⋅ ( x + d ) = x 2 + ( b + d ) x + bd
1
k
n1 !n2 ! nk !
3
⎝ 2⎠ 0
( ax + b ) ⋅ ( cx + d ) = acx 2 + ( ad + bc ) x + bd CONSTANTES sen (α ± β ) = sen α cos β ± cos α sen β -1
( a + b ) ⋅ ( c + d ) = ac + ad + bc + bd π = 3.14159265359… 2
cos (α ± β ) = cos α cos β ∓ sen α sen β
-2
se nh x
e = 2.71828182846…
-3 co sh x
( a + b ) = a3 + 3a 2b + 3ab2 + b3 tg α ± tg β
3 1 tgh x
tg (α ± β ) =
-4
-5 0 5
TRIGONOMETRÍA
1 ∓ tg α tg β
( a − b ) = a3 − 3a 2b + 3ab2 − b3
3 0
CO 1 FUNCIONES HIPERBÓLICAS INV
sen θ = cscθ = sen 2θ = 2sen θ cosθ
( a + b + c ) = a 2 + b2 + c 2 + 2ab + 2ac + 2bc
2 HIP
CA
sen θ
1
-1
arc sen x
arc cos x
arc tg x cos 2θ = cos 2 θ − sen 2 θ (
senh −1 x = ln x + x 2 + 1 , ∀x ∈ )
cosθ = secθ =
( a − b ) ⋅ ( a + ab + b ) = a − b ( )
-2
2 tg θ
2 2 3 3
cosθ
-3 -2 -1 0 1 2 3
HIP tg 2θ = cosh −1 x = ln x ± x 2 − 1 , x ≥ 1
sen θ CO 1 − tg 2 θ
( a − b ) ⋅ ( a3 + a 2 b + ab2 + b3 ) = a 4 − b4 tg θ = = ctg θ =
1
1 ⎛1+ x ⎞
cosθ CA tg θ 1 tgh −1 x = ln ⎜ ⎟, x < 1
( a − b ) ⋅ ( a 4 + a3b + a 2 b2 + ab3 + b 4 ) = a5 − b5 sen 2 θ = (1 − cos 2θ ) 2 ⎝ 1− x ⎠
2
⎛ ⎞ π radianes=180 1 ⎛ x +1 ⎞
ctgh −1 x = ln ⎜
n
1
( a − b ) ⋅ ⎜ ∑ a n − k b k −1 ⎟ = a n − b n ∀n ∈ cos 2 θ = (1 + cos 2θ ) ⎟, x > 1
2 ⎝ x −1 ⎠
⎝ k =1 ⎠ 2
1 − cos 2θ ⎛ 1 ± 1 − x2 ⎞
HIP tg 2 θ = sech −1 x = ln ⎜ ⎟, 0 < x ≤ 1
CO 1 + cos 2θ ⎜ x ⎟
⎝ ⎠
θ ⎛1 x2 + 1 ⎞
csch −1 x = ln ⎜ + ⎟, x ≠ 0
CA ⎜x x ⎟
⎝ ⎠