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CalculusCalculus10th Edition

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Chapter 12.5, Problem 23E
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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
1 views

Finding CurvatureIn Exercises 23–28, find the curvature of the plane curve at the given value of the parameter.

r ( t ) = 4 t i − 2 t j ,       t = 1

To determine

To calculate: The curvature of the plane curve at the given value of the parameter r(t)=4 t i−2 t j , t=1.

Explanation

Given:

The curve is r(t)=4 t i−2 t j , t=1.

Formula Used:

The curvature of the curve at t as: K=‖T′(t)‖‖r′(t)‖ where T(t)=r′(t)‖r′(t)‖.

Calculation:

Consider the provided curve,

r(t)=4 t i−2 t j

Now, differentiate the provided curve r(t) and find the absolute value of r′(t),

r′(t)=4 i−2 j

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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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