Chapter 16.6, Problem 4E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Identify the surface with the given vector equation.

**4. r**(*u*, *v*) = *u*^{2} **i** + *u* cos *v* **j** + *u* sin *v* **k**

To determine

**To identify:** The surface with the vector equation

Explanation

**Given data:**

The vector equation is given as follows.

**Formula used:**

Write the expression for circular paraboloid that symmetric to the *x*-axis.

Write the vector equation as follows.

Write the parametric equations from the vector equation as follows.

Take square on both sides of the symmetric expression

Take square on both sides of the symmetric expression

Add the expressions

Sect-16.1 P-1ESect-16.1 P-2ESect-16.1 P-3ESect-16.1 P-4ESect-16.1 P-5ESect-16.1 P-6ESect-16.1 P-7ESect-16.1 P-8ESect-16.1 P-9ESect-16.1 P-10E

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