(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Calculus Questions - HELP

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