Exercicios Lagrange Resolvidos

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  • 8/16/2019 Exercicios Lagrange Resolvidos

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    QUESTÃO 1:F(x,y)= xy x^2+y^2=8

    Fx: y=L2x fy: x=L2y

      y/2x=x/2y  x=y

    x^2+x^2=82x^2=8x= +- 2 y= +-2

    Pontos: {-2,-2 {-2,2 {2,2 {2,-2

    F(x,y)= -2! (-2)= +"F(x,y)= -2!2= -"

    F(x,y)= 2!2="F(x,y)=2! (-2)= -"

    PO#TO $%&'$O= " PO#TO $#'$O= -"

    QUESTÃO 2:xy^2 x^2+y^2=Fx: y^2=L2x Fy: 2xy=L2y

      y^2/2x=2xy/2y  y^2=2x^22x^2+x^2=x^2=x= +-1

    P* * o .:y^2=2x^2y^2=2!(+-1)^2y= =+- *0 3*3 34 2

    1!2=2

    -1!2= -2

    PO#TO $%&'$O 2 PO#TO $#'$O -2

    QUESTÃO xy x^2+y^2=25fx: y=L2x fy: x=L2y  x=y

    &^2+x^2=25

    2x^2=25x= +- *0 3*3 34 25/2 y= +-*0 3*3 34 25/2

  • 8/16/2019 Exercicios Lagrange Resolvidos

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    -*0 3*3 34 25/2 !(- *0 3*3 34 25/2)= 25/2*0 3*3 34 25/2 !(- *0 3*3 34 25/2 )= -25/2PO#TO $%&'$O: 25/2 PO#TO $#'$O 25/2

    O6S: L= 793