Labware - MA35 Multivariable Calculus - Three Variable Calculus



Slice Curves & Surfaces (Page: 1 | 2 | 3 )


We begin the study of a function f of three variables x, y, and z in a rectangular domain by fixing two of the variables to produce a function of a single variable defined over an interval.

The collection of points (x,y0,z0,f(x,y0,z0)) is the graph of the slice function over y = y0, z = z0, called the slice curve for y = y0, z = z0.

By fixing one of the three variables, for example z = z0, we obtain a function of the remaining two variables x and y. The graph of this function is called the z0-slice surface.



  • Type in the function f(x,y,z) = 2xyz/(x2 + y2 + z2) What happens to slice curves that pass through the origin? You may want to change the resolution of the graph by increasing the number of x, y, and z steps.