EJERCICIO 3 PARTE 1

xHy x-zLyHy x-zLzHy x-zLx-z

y

x-z

-x-z

y

xI9 x2 + 4 y2 + 36 z2 - 36M ayI9 x2 + 4 y2 + 36 z2 - 36M azI9 x2 + 4 y2 + 36 z2 - 36M a18 a x

8 a y

72 a z

xHHx yL + Hy zL - 1L byHHx yL + Hy zL - 1L bzHHx yL + Hy zL - 1L bb y

b Hx + zL

b y

SolveA9x-z y == H18 a xL + Hb yL, x-z == H8 a yL + Hb Hx + zLL, -x-z y == H72 a zL + Hb yL,9 x

2+ 4 y

2+ 36 z

2== 36, Hx yL + Hy zL == 1=, 8x, y, z, a, b

EJERCICIO 3 PARTE 2

xHx + y + zLyHx + y + zLzHx + y + zL1

1

1

xIx2 - y2 - zM ayIx2 - y2 - zM azIx2 - y2 - zM a2 a x

-2 a y

-a

xIx2 + z2 - 4M byIx2 + z2 - 4M bzIx2 + z2 - 4M b2 b x

0

2 b z

minimo

maximo

EJERCICIO 4

NAIntegrateAx5 y3 xy, 8x, 0, 1

Plot3DAx5 y3 xy, 8x, 0, 1