Domain, Range & Function Graphs 2D
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Slice Curves in Cylindrical Coordinates 2D Rectangular Coordinates
Spherical
Coordinates
Parametric
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For every point (r0,θ0,z0) in the
domain of a function f, the intersection of the graph of f with the
vertical plane r = r0, θ = θ0 will be the (r0,θ0)-slice
curve (r0,θ0,z,f(r0,θ0,z)).
The domain of the r0-slice curve is the set of z for which (r0,θ0,z)
is in the domain of f.
Similarly we define the (θ0,z0)-slice curve to be
(r,θ0,z0,f(r,θ0,z0)) for
all r such that (r,θ0,z0) is in the domain of f,
and we define the (r0,z0)-slice curve to be (r0,θ,z0,f(r0,θ,z0))
for all θ such that (r0,θ,z0) is in the domain of
f.
We can obtain an arbitrary line through [r0,θ0,z0]
as (x + t cos(θ0), y0 + t sin(θ0), z0
+ mt) for various choices of m, and then the slice curve is
(x0 + t cos(θ0), y0 + t sin(θ0),
z0 + mt,f((x0 + t cos(θ0), y0
+ t sin(θ0), z0 + mt))).
Slice Surfaces in Cylindrical Coordinates Rectangular Coordinates Spherical
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For every point (r0,θ0,z0) in the
domain of a function f, the intersection of the graph of f with the
vertical hyperplane z = z0, will be the z0-slice
surface (r,θ,z0,f(r,θ,z0)). The domain of
the z0-slice surface is the set of (r, θ) for which (r,θ,z0)
is in the domain of f.
Similarly we define the θ0-slice surface to be (r,θ0,z,f(r,θ0,z))
for all (r, z) such that (r,θ0,z) is in the domain of f, and
we define the r0-slice surface to be (r0,θ,z,f(r0,θ,z))
for all (θ, z) such that (r0,θ,z) is in the domain of f.
Level Sets and Contours in Cylindrical Coordinates
2D
Rectangular Coordinates
Spherical Coordinates
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