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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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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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