Chapter 16.6, Problem 15E

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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.

**15. r**(*u*, *v*) = (*u*^{3} − *u*) **i** + *v*^{2} **j** + *u*^{2} **k**

To determine

**To match:** The equation

Explanation

**Given data:**

The given vector equation as follows.

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

Write the vector equation as follows.

Write the parametric equations from the vector equation as follows.

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

If the parameter
*x*- and *z*-parameters become constant and only the parameter *y* is a variable.

Therefore, each grid curve is contained in a straight line parallel to the *y*-axis when the parameter

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