Answer to Question #51992 in Calculus for john

Question

1)Use the method of Language multipliers,find the maximum value of the function f(x,y,z)=xyz subject to the constraint g(x,y,z)=2xy+2yz+zx=12,x>0,y>0,z>0
2)Use polar coordinates to find the volume of the soild inside the sphere x^(2)+y^(2)+z^(2)=16 and outside the cylinder x^(2)+y^(2)=4
3)Given the vector flied
F(x,y,z)=(y^(2)-4z,2xy +6yz ,-4x+5y^(2))
a)Find a potential function of F
b)Evaluate the line intergral