Chapter 13.3, Problem 10E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Graph the curve with parametric equations *x* = sin *t*, *y* = sin 2*t*, z = sin 3*t*. Find the total length of this curve correct to four decimal places.

To determine

**To plot:** The curve with parametric equations

Explanation

**Given data:**

Consider the parametric equations.

Draw the required curve by using parametric equations in equations (1), (2) and (3) as shown in Figure 1.

The different view of curve in Figure 1 is drawn as shown in Figure 2.

Include a plot showing a tube of radius 0.07 around the curve as shown in Figure 3.

The complete curve is given by parameter interval

The vector equation

Substitute
*x*,
*y*, and
*z*,

Differentiate the equation with respect to *t*.

Take magnitude on both sides of the equation

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