The equation for a 3D cylinder as described in Murray Spiegel's Advanced Calculus, specifically in solved problem 10.18, is x^2 + y^2 = ax. This equation represents a cylinder where the cross-section in the x-y plane is a circle, and the z-coordinate is arbitrary, allowing for circular cross-sections at any height. Thus, the cylinder extends infinitely along the z-axis, confirming its three-dimensional nature.
PREREQUISITESStudents of calculus, geometry enthusiasts, and educators seeking to clarify the relationship between 2D equations and their 3D counterparts will benefit from this discussion.
No, it's a 3D object, with z being arbitrary. If you look at the trace of this cylinder in the x-y plane (i.e., z = 0), you get a circle. For any z = k, some constant, you also get a circle, but this time in the plane z = k.coverband said:1. In Murray Spiegel's Advanced Calculus, in solved problem 10.18 he describes a cylinder as having equation x^2 + y^2 = ax. Surely this equation is for a 2-D object. Whats going on as a cylinder is 3D?