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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 3.8, Problem 17E

(a)

To determine

**To find:** The linear density at

Expert Solution

The linear density at

**Given:**

The mass of the part of the metal rod which lies between its left end and a point *x* m away from the right end is

**Calculation:**

The mass of the metal rod is,

The linear density of the rod is the derivative of the mass and hence

The linear density at

(b)

To determine

**To find:** The linear density at

Expert Solution

The linear density at

From part (a), the linear density of the rod is,

The linear density at

The linear density at

(c)

To determine

**To find:** The linear density at

Expert Solution

The linear density at

From part (a), the linear density of the rod is,

The linear density at

Notice that the density function is an increasing function. Therefore, the density of the rod is highest at its right end and lowest at its left end.