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Calculus Questions - HELP

  1. Dec 17, 2003 #1
    Calculus Questions - HELP!!!!!

    1. Consider the cube determined by the planes x=-1, x=3, y=5, y=9,
    z=0, and z=4.

    a) Give the coordinates of the eight vertices and center of
    the cube.

    b) Determine an equation of the largest sphere contained in
    the cube.

    c) Determine an equation of the largest sphere that would fit
    between the sphere found in (b) and the cube.

    2. Determine an equation of a plane that intersects the plane
    x+y+z=3 at an angle of 60 degrees.

    3. a) Determine an equation of the tangent plane to the surface
    given by x^2*y+y^2*z+z^2*x=1 at the point (1,0,1).

    b) Determine an equation of the line that is normal to the
    surface given by x^2*y+y^2*z+z^2*x=1 at the point (1,0,1).

    4. Prove that u+v+w=0, then u*v=v*w, and u*w=w*v. What is the
    geometric interpretation of these relationships?

    5. Suppose f(x,y)=A*X^3+B*X*Y+C*Y^2, where A, B, and C are
    constants. For what values of A, B, and C does f have a
    critical value at (-2,1)? Determine what type of critical
    point it is.

    6. Determine the maximum value of f(x,y,z)=(x*y*z)^2 subject to
    the constraint x^2+y^2+z^2=c^2, where c is not equal to zero.
     
  2. jcsd
  3. Dec 18, 2003 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Why is this not in the homework section?

    Presuming they are homework, show us what you have done on these problems.
     
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