   Chapter 16.6, Problem 5E

Chapter
Section
Textbook Problem

Identify the surface with the given vector equation. r ( s , t ) = 〈 s cos t , s sin t , s 〉

To determine

To identify:

The surface with the given vector equation

Explanation

1) Concept:

If ru, v is a vector valued function on a region D in the uv- plane,

ru, v=xu, vi+yu, vj+zu, vk

So x, y, and z,  the component functions of r, are functions of the two variables u & v  with the domain  D. The set of all points x, y, z in R3 such that

x=xu, v, y=yu, v, z=zu, v

And u, v varies throughout  D which is called a parametric surface S and x=xu, v, y=yu, v, z=zu, v are called parametric equations of S

2) Given:

rs, t=scost, ssint, s

3) Calculations:

Given vector equation is,

rs, t=scos

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