Formulario de calculo

Formulario de Cálculo Diferencial
(a+b)⋅(a2 −ab+b2)=a3 +b3
(a+b)⋅(a3 −a2b+ab2 −b3)=a4 −b4
(a+b)⋅(a4 −a3b+a2b2 −ab3 +b4)=a5 +b5(a+b)⋅(a5 −a4b+a3b2 −a2b3 +ab4 −b5)=a6 −b6
θ
sen cos 0 1
tg ctg sec 0 ∞ 1
csc
Gráfica4.Lasfuncionestrigonométricasinversas arcctgx , arcsecx , arccscx :
senα+senβ =2sen1(α+β)⋅cos1(α−β) 22
eIntegral VER.4.3 Jesús Rubí Miranda (jesusrubim@yahoo.com)
45 1 2 1 2 1 1 2 2 60􏰂 3 2 12 3 1 3 2 2 3 90􏰂 1 0 ∞ 0 ∞ 1
3
cosα+cosβ=2cos1(α+β)⋅cos1(α−β) 22
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⎛n k+1 ⎞
(a+b)⋅⎜∑(−1) an−kbk−1⎟=an +bn ∀n∈􏰀impar
11 cosα−cosβ=−2sen α+β ⋅sen α−β
⎧a si a ≥ 0
-1
arc ctg x arc sec x arc csc x
⎩−a si a < 0 a = −a
SUMASYPRODUCTOSy=∠tgx y∈ − ,
a ≤ a y − a ≤ a a≥0ya=0⇔a=0
a1+a2 +􏰁+an =
a
k
y=∠ctgx=∠tg1 x
y∈ 0,π y∈ 0,π
IDENTIDADESTRIGONOMÉTRICAS
1
senα⋅senβ= ⎡cos(α−β)−cos(α+β)⎤
ab = a b ó ∏a = k
a+b≤a+bó∑a ≤ k
a
k∑(ak +bk)=∑ak +∑bk k=1 k=1 k=1
ap⋅aq =ap+q p
k k−1 n 0 k=1
sen(θ+2π)=senθ
cos(θ+2π)=cosθ
tg (θ + 2π ) = tgθ
sen(θ+π)=−senθ coshx
a =ap−q aq
1.5 1 k=1 2 0.5
x −x coshx=e +e
(ap)q =apq
= n (a +l ) 2
tgh x = =
x −x ex +e−x
(a⋅b)p =ap⋅bp
nn
∑ark−1 =a1−r =a−rl
0 -0.5 -1
cos(θ+π)=−cosθ tg (θ + π ) = tgθ
ctgh x =
x−x 1e+e
⎛a⎞p ap ⎜⎟=p ⎝b⎠ b
k=1 1−r 1−r n
=
tghx ex −e−x
ap/q=qaplog N=x⇒ax =N
-2
-8 -6 -4 -2 0 2 4 6 8
senθ+nπ = −1 senθ cos(θ+nπ)=(−1)n cosθ tg (θ + nπ ) = tgθ
x −x
a
loga MN = loga M + loga N
k=1 6 n1
sen(nπ)=0 cos(nπ)=(−1)n tg (nπ ) = 0
senhx e−esenh:􏰃→􏰃
log M = log M − log N aNa a
n415 4 3
∑k =30(6n +15n +10n −n)
loga Nr =rloga N
log N=logbN=lnN
k=1 1+3+5+􏰁+(2n−1)=n2
2n+1 n
sen⎛ π⎞=(−1) sech:􏰃→ 0,1
VALOR ABSOLUTO
0
sen (α ± β ) cosα⋅cosβ
nnc=nc ∑cak =c∑ak
[ ]
⎡ π π⎤
1+ctg2θ=csc2θ tg2θ+1=sec2θ
cosα⋅cosβ= ⎡cos(α−β)+cos(α+β)⎤ 2⎣⎦
∏ k=1 k=1
(x+b)⋅(x+d)=x2 +(b+d)x+bd
n1!n2!􏰁nk ! CONSTANTES
⎝⎠ sen(α±β)=senαcosβ±cosαsenβ
a...