Math 119 Formula Sheet

Math 119 Formula Sheet - Math 119 Final Exam Formulae dn (u...

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Unformatted text preview: Math 119 Final Exam Formulae dn (u ) = nun−1 du d (f (x)g (x)) = f ′ (x)g (x) + g ′ (x)f (x) dx 1 d (ln u) = du u d f (x) f ′ (x)g (x) − g ′ (x)f (x) ( )= dx g (x) [g (x)]2 d g ′ (u) (ln(g (u))) = du g (u) du (a ) = au ln a du du (e ) = eu du d 1 (logb u) = du u ln b un+1 +C n+1 d g (u) (e ) = g ′ (u)eg(u) du un du = d (sin u) = cos u du u−1 du = ln |u| + C d (cos u) = − sin u du eu du = eu + C d (tan u) = sec2 u du cos u du = sin u + C d (csc u) = − csc u cot u du sin u du − cos u + C d (sec u) = sec u tan u du tan u du = − ln | cos u| + C d (cot u) = − csc2 u du cot u du = ln | sin u| + C udv = uv − v du du = u + C sin θ = Op Hyp csc θ = 1 sin θ cos θ = Adj Hyp sec θ = 1 cos θ tan θ = Op Adj cot θ = 1 tan θ sin2 x + cos2 x = 1 a b a c = a b+ c a logb ( ) = logb a − logb c c ab = a b− c ac logb ac = c logb a (ab )c = abc log a = log10 a logb (ac) = logb a + logb c ln a = loge a a logb ( ) = logb a − logb c c logb a = average value = 1 b−a b a f (x)dx volume (revolution) = D = fxy (a, b)fyy (a, b) − [fxy (a, b)]2 f ′ (x) = limh→o ln a ln b b a π [f (x)]2 dx F (x, y, z, λ) = f (x, y, z ) + λg (x, y, z ) f (x + h) − f (x) h Geometric Sequence: an = a1 (r)n−1 , n = 1, 2... − Sum of First n terms: Sn = Σn=01 a1 ri , = i Sum of a Geometric Series: E (x) = µ = σ= b a a1 1−r xf (x)dx a1 (rn − 1) , n = 1, 2... (r − 1) V ar(x) = b a x2 f (x)dx − µ2 V ar(x) Uniform Distribution f (x) = 1 [a, b] b−a µ= a+b 2 b−a σ= √ 12 Exponential Distribution f (x) = ae−ax µ= 1 a σ= Standard Normal Distribution (use tables) µ=0 σ=1 1 a ...
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Math 119 Formula Sheet - Math 119 Final Exam Formulae dn (u...

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