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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Match the equations with the graphs labeled I–VI and give reasons for your answers. Determine which families of grid curves have u constant and which have v constant.

18. x = sin u, y = cos u sin v, z = sin v

images

To determine

To match: The parametric equations x=sinu,y=sinusinv,z=sinv with the graphs labeled I-VI in the textbook and to explain the reason for the combination.

Explanation

Given data:

Write the given parametric equations as follows.

x=sinu,y=sinusinv,z=sinv (1)

The graphs are labeled in the textbook from I to VI.

Determination of grid curves when v is constant:

Consider the parameter v=v0 .

Substitute v0 for v in equation (1),

x=sinu,y=sinusinv0,z=sinv0

If the parameter v is held constant, the parameter z becomes constant.

The expression x=sinu,y=sinusinv0,z=sinv0 represents an ellipse that contains in the horizontal plane

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Chapter 16 Solutions

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