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8/16/2019 Exercicios Lagrange Resolvidos
1/2
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
2/2
-*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