Adaptación plantas y animales al medio ambiente preguntas
Formulario de
Cálculo Diferencial e Integral
VER.4.3
Jesús Rubí Miranda (jesusrubim@yahoo.com) http://mx.geocities.com/estadisticapapers/ http://mx.geocities.com/dicalculus/
VALOR ABSOLUTO
⎧ a si a ≥ 0 a =⎨
⎩ − a si a < 0 a = −a
n
∏a
a+b ≤ a + b ó
n
∑ ca
k =1
n
k =1
k =1
n
k
≤ ∑ ak
∑(a
k =1
∑(a
csc
1
1
∞
∞
323 2
321 3
2
2
1
1
1 21 2
313
2 23
3 2 12
0
0
1
1
∞
∞
0
12
y = ∠ sen x y = ∠ cos x
⎡ π π⎤ y ∈ ⎢− , ⎥
⎣ 2 2⎦ y ∈ [ 0, π ] y∈ −
k =1
n
k =1
k =1
k
+ bk ) = ∑ ak + ∑ bk
k
− ak −1 ) = an − a0
n
∑ ar
k −1
k =1
,
22
log a MN = log a M + log a N
M
log a
= log …ver más…
5
=
sen α + sen β sen α − sen β
4
0
2
n
Gráfica 4. Las funciones trigonométricas inversas arcctg x , arcsec x , arccsc x :
1
1 y ∈ [ 0, π ] x 1
⎡ π π⎤ y = ∠ csc x = ∠ sen y ∈ ⎢− , ⎥ x ⎣ 2 2⎦
Gráfica 1. Las funciones trigonométricas: sen x , co s x , tg x :
= c ∑ ak
= ap ⋅bp
⎛
sec
y = ∠ sec x = ∠ cos
k =1
p
log a N =
ctg
1. 5
ap
⎛a⎞
⎜⎟=p b ⎝b⎠
=a
tg
0
cos
1 y = ∠ ctg x = ∠ tg x k =1
n
q
q
+ an = ∑ ak
n
n
0
30
45
60
90
sen
y = ∠ tg x
∑ ⎡ a + ( k − 1) d ⎤ = 2 ⎡ 2a + ( n − 1) d ⎤
⎣
⎦
⎣
⎦
( a p ) = a pq
a
k =1
k =1
ap
= a p−q aq p/q
k
θ
n
n
n
a p ⋅ a q = a p+q
p
par
k =1
n
∑a
⎞ a n − k b k −1 ⎟ = a n − b n ∀ n ∈
⎠
SUMAS Y PRODUCTOS k +1
n
= ∏ ak
k
impar
∑ c = nc
EXPONENTES
(a ⋅ b)
⎛
n
( a + b ) ⋅ ⎜ ∑ ( −1) a1 + a2 +
a ≥0y a =0 ⇔ a=0
k =1
⎛n
⎞
k +1
( a + b ) ⋅ ⎜ ∑ ( −1) a n− k b k −1 ⎟ = a n + b n ∀ n ∈
⎝ k =1
⎠
⎝ k =1
a ≤ a y −a≤ a
ab = a b