   Chapter 16.6, Problem 6E

Chapter
Section
Textbook Problem

Identify the surface with the given vector equation.6. r(s, t) = ⟨3 cos t, s, sin t⟩, − 1 ⩽ s ⩽ 1

To determine

To identify: The surface with the vector equation r(s,t)=3cost,s,sint,1s1 .

Explanation

Given data:

The vector equation is given as follows.

r(s,t)=3cost,s,sint,1s1

Formula used:

Write the expression for elliptical cylinder that corresponds to the y-axis.

x2a2+zb22=yc (1)

Write the vector equation as follows.

r(s,t)=3cost,s,sint,1s1

Write the parametric equations from the vector equation as follows.

x=3cost,y=s,z=sint

Rewrite the x-parameter as follows.

x=3costx3=cost

Take square on both sides of the expression.

(x3)2=cos2t (2)

Rewrite the z-parameter as follows.

z=sint

Take square on both sides of the expression.

z2=sin2t (3)

Write the expression from equation (2) and (3) as follows

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