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CalculusCalculus10th Edition

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Chapter 12.5, Problem 87E
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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Problem 74E
Problem 75E
Problem 76E
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Problem 79E
Problem 80E
Problem 81E
Problem 82E
Problem 83E
Problem 84E
Problem 85E
Problem 86E
Problem 87E
Problem 88E
Problem 89E
Problem 90E
Problem 91E
Problem 92E
Problem 93E
Problem 94E
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem
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57095-12.5-87E-Question-Digital.docx

True or False? In Exercises 85-88, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

The curvature of a line is 0.

To determine

The statement: “The curvature of a line is 0” is true or false.

Explanation

Consider the provided statement: “The curvature of a line is 0”.

According to definition of curvature, the curvature is the measure of sharpness of bend in any curve.

A straight line doesn’t have any bend thus its curvature becomes zero.

For example, take a line y=mx.

Apply the formula for the curvature,

K=|y″|[1+(y′)2]32

Double differentiate y with respect to x, That is,

<

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Sect-12.1 P-1ESect-12.1 P-2ESect-12.1 P-3ESect-12.1 P-4ESect-12.1 P-5ESect-12.1 P-6ESect-12.1 P-7ESect-12.1 P-8ESect-12.1 P-9ESect-12.1 P-10E
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