Questions from General Calculus

Q: Use a computer to graph the surface, the tangent plane,

Use a computer to graph the surface, the tangent plane, and the normal line on the same screen. Choose the domain carefully so that you avoid extraneous vertical planes. Choose the viewpoint so that y...

Q: Use a computer to graph the surface, the tangent plane,

Use a computer to graph the surface, the tangent plane, and the normal line on the same screen. Choose the domain carefully so that you avoid extraneous vertical planes. Choose the viewpoint so that y...

Q: At what point on the ellipsoid x2 + y2 + 2z2 =

At what point on the ellipsoid x2 + y2 + 2z2 = 1 is the tangent plane parallel to the plane x + 2y + z = 1?

Q: Are there any points on the hyperboloid x2 - y2 - z2

Are there any points on the hyperboloid x2 - y2 - z2 = 1 where the tangent plane is parallel to the plane z = x + y?

Q: Show that the ellipsoid 3x2 + 2y2 + z2 = 9 and

Show that the ellipsoid 3x2 + 2y2 + z2 = 9 and the sphere x2 + y2 + z2 - 8x - 6y - 8z + 24 = 0 are tangent to each other at the point (1, 1, 2). (This means that they have a common tangent plane at th...

Q: Show that every plane that is tangent to the cone x2 +

Show that every plane that is tangent to the cone x2 + y2 = z2 passes through the origin.

Q: At what points does the normal line through the point (1

At what points does the normal line through the point (1, 2, 1) on the ellipsoid 4x2 + y2 + 4z2 = 12 intersect the sphere x2 + y2 + z2 = 102?

Q: The speed of sound traveling through ocean water with salinity 35 parts

The speed of sound traveling through ocean water with salinity 35 parts per thousand has been modeled by the equation C = 1449.2 + 4.6T - 0.055T2 + 0.00029T3 + 0.016D where C is the speed of sound (...

Q: Suppose that the equation F (x, y, z)

Suppose that the equation F (x, y, z) = 0 implicitly defines each of the three variables x, y, and z as functions of the other two: z = f (x, y), y = t (x, z), x = h (y, z). If F is differentiable and...

Q: Find the local maximum and minimum values and saddle point(s

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the impor...