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Examples: Construct examples of the thing(s) described in

the following. Try to find examples that are different than

any in the reading.

(a) A region in R3that is most easily expressed with rectangular

coordinates.

(b) A region in R3that is most easily expressed with

cylindrical coordinates.

(c) A region in R3that is most easily expressed with

spherical coordinates.

Short Answer

Expert verified

Part (a) (x,y,z)R3x2+y2+z2=1.

Part (b) (r,θ,z)R3r2+z2=1.

Part (c)(ρ,θ,ϕ)R3ρ2=1.

Step by step solution

01

Part (a) Step 1: Find an example that is different than any in the reading.

A regionR3in which rectangular coordinates can be stated is,

(x,y,z)R3x2+y2+z2=1.

This is a sphere equation with a radius 1

02

Part (b) Step 1: Find an example that is different than any in the reading. 

A regionR3in which cylindrical coordinates can be stated is,

(r,θ,z)R3r2+z2=1.

This is a sphere equation with a radius1

03

Part (c) Step 1: Find an example that is different than any in the reading.

A regionR3in which cylindrical coordinates can be stated is,

(ρ,θ,ϕ)R3ρ2=1.

This is a sphere equation with a radius1

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