Formaulario
CÁLCULO DIFERENCIAL
VER.3.3
E INTEGRAL
Por Jesús Rubí M.
http://mx.geocities.com/estadisticapapers/
( a + b ) ⋅ ( a 2 − ab + b2 ) = a 3 + b3
( a + b ) ⋅ ( a 4 − a3b + a 2b 2 − ab3 + b 4 ) = a5 + b5
θ
0
30
n
k +1
( a + b ) ⋅ ∑ ( −1) a n −k b k −1 = a n + b n ∀2n − 1
k =1
SUMAS Y PRODUCTOS
45
a1 + a2 +
VALOR ABSOLUTO
n
+ an = ∑ ak
a≤ a y −a ≤ a
k =1
ab = a b ó
k
+ bk ) = ∑ ak + ∑ bk
n
n
∏a
k =1
= c∑ ak
k =1
n
k
= ∏ ak
n
∑ (a
k =1
n
n
k =1
n
n
k
n
k =1
k =1
− ak −1 ) = an − a0
LOGARITMOS
log a N = x ⇒ a x = N
1+ 3 + 5 +
∑a
k =1
k
≤ ∑ ak
k =1
EXPONENTES
a p ⋅ a q = a p+q
ap
= a p−q
aq
(a )
pq
(a ⋅b)
=a
p
pq
= a p⋅bp
p
ap
a
=p
b
b
q
a p/q = a p
log a MN = log a M + log a N
log a N =
n
k =1
y∈ −
-1
ππ
,
22
∀n ∈
arc ctg x
arc sec x
arc csc x
-2
-5
0
y ∈ 0, π
2
sen θ + cos 2 θ = 1
1 + ctg 2 θ = csc 2 θ
sen (θ + 2π ) = sen θ
cos (θ + 2π ) = cosθ
tg (θ + 2π ) = tg θ
sen (θ + π ) = − sen θ
-0.5
cos (θ + π ) = − cosθtg (θ + π ) = tg θ
-1
sen x
cos x
tg x
-1.5
-2
-8
-6
-4
-2
0
2
4
6
2.5
n
tg ( nπ ) = 0
-0.5
-1
-1.5
csc x
sec x
ctg x
-6
-4
-2
0
2
4
6
8
Gráfica 3. Las funciones trigonométricas inversas
arc sen x, arc cos x, arc tg x.
2n + 1
tg
π=∞
2
π
sen θ = cos θ −
2
π
cosθ = sen θ +
2
sen (α ± β ) = sen α cos β ± cos α sen β
4
3
2
cos (α ± β ) = cos α cos β ∓ sen α sen β
1
tg α ± tg β
tg (α ± β ) =
1 ∓ tg α tg β
sen 2θ = 2 sen θ cos θ
0
-1
arc sen x
arc cos x
arc tg x
CO
-2
-3
tg (θ + nπ ) = tg θ
sen ( nπ ) = 0
n
2n + 1
sen
π = ( −1)
2
2n + 1
cos
π=0
2
0
π radianes=180
cos (θ + nπ ) = ( −1)cosθ
n
cos ( nπ ) = ( −1)
0.5
1
cscθ =
sen θ
1
secθ =
cos θ
1
ctg θ =
tg θ
sen (θ + nπ ) = ( −1) sen θ
n
8
Gráfica 2. Las funciones trigonométricas csc x, sec x,
ctg x.
-2.5
-8
-2
-1
0
1
5
IDENTIDADES TRIGONOMÉTRICAS
1
CA
senh x =
0
y ∈ [ 0, π ]
2
θ
FUNCIONES HIPERBÓLICAS
tg ( −θ ) = − tg θ
2
1
1.5
HIP
cos( −θ ) = cosθ
3
0
+ ( 2n − 1) = n 2
TRIGONOMETRÍA
CO
sen θ =
HIP
CA
cos θ =
HIP
sen θ CO
=
tg θ =
cos θ CA
tg 2 θ + 1 = sec 2 θ
sen ( −θ ) = − sen θ
4
1
-2
( a + b ) ⋅ ( a − b ) = a2 − 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 ) = a 3 + 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
a − b ) ⋅ ( a 2 + ab + b 2 ) = a 3 − b 3
(
( a − b ) ⋅ ( a 3 + a 2b + ab 2 + b3 ) = a 4 − b 4
( a − b ) ⋅ ( a 4 + a 3b + a 2b 2 + ab3 + b 4 ) = a 5 − b5
( a − b ) ⋅ ∑ a n −kb k −1 = a n − b n
∞
0
1
1
(α + β ) ⋅ cos (α − β )
2
2
1
1
sen α − sen β = 2 sen (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 sen (α + β ) ⋅ sen (α − β )
2
2
sen (α ± β )
tg α ± tg β =
cos α ⋅ cos β
1
sen α ⋅ cos β = sen (α − β ) + sen (α + β )
2
1
sen α ⋅ sen β = cos (α − β ) − cos (α + β )
2
1
cos α ⋅ cos β = cos (α − β ) + cos (α + β )
2
tg α + tg β
tg α ⋅ tg β =
ctg α + ctg β
3
1
k =1
a ⋅ ( c + d ) = ac + ad
2
0.5
n
n!
, k≤n
=
k ( n − k )!k !
n
n n− k k
n
( x + y) = ∑ x y
k =0 k
log10 N = log N y log e N = ln N
ALGUNOS PRODUCTOS
3
Gráfica 4. Las funciones trigonométricas inversas
arc ctg x, arc...
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