Chapter 16.6, Problem 13E

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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.

**13. r**(*u*, *v*) = *u* cos *v* **i** + *u* sin *v* **j** + *v* **k**

To determine

**To match:** The equation

Explanation

**Given data:**

The given vector equation as follows.

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
*xy*-plane is circular with

Thus, each grid curve is a helix when the parameter

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