formulas calculo integral y diferencial

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

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formulas calculo integral y diferencial

  1. 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 2Cálculo 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 + b5e 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 ∞ 1http://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⎤ 1http://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 TRIGONOMÉTRICASa ≤ 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− xa 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 xa 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) nlog a k =1 2 N tgh : → −1,1 ∑ k 4 = 30 ( 6n5 + 15n4 + 10n3 − n ) n 1 tg ( nπ ) = 0 1.5log 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 xa ⋅ ( 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 ⎟ ⎝ ⎠

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