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Coordenadas Polares

Coordenadas Polares. y. r 2 = x 2 + y 2. P. y. cos  = x/r.  = arctg y/x. r. sen  = y/r. . x. x. retang.  polares. x = r cos . polares  retang. y = r sen . Curvas em Coordenadas Polares. y. P. r.  2. . .  1. x. r = f ().  1     2.

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Coordenadas Polares

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  1. Coordenadas Polares y r2 = x2 + y2 P y cos  = x/r  = arctg y/x r sen  = y/r  x x retang.  polares x = r cos  polares retang. y = r sen 

  2. Curvas em Coordenadas Polares y P r 2   1 x r= f () 1   2

  3. Regiões em Coordenadas Polares y R r= f2 () 2 1 x f1 ()  r  f2 () r= f1 () 1   2

  4. Integrais Duplas em Coordenadas Polares y Rk = (r12 - r22)( - )/2 R = [(r1 + r2)/2](r) r2 unidade de área: Rk Rk r1   x

  5. Cálculo da Integral Dupla em Coordenadas Polares R:     r1 ()  r  r2 ()

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