Chapter 16.6, Problem 17E

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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.

**17.** *x* = cos^{3}*u* cos^{3}*v*, *y* = sin^{3}*u* cos^{3}*v*, *z* = sin^{3}*v*

To determine

**To match:** The parametric equations

Explanation

**Given data:**

Write the given parametric equations as follows.

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

**Determination of grid curves when**
** is constant:**

If the parameter
*z* becomes constant and the grid curves lies in a horizontal planes.

Therefore, when the parameter

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