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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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57095-12.5-21E-Question-Digital.docx

Finding Curvature In Exercises 19–22, find the curvature K of the curve, where s is thearc length parameter.

Helix in Exercise 17: r ( t ) = 2 cos t , 2 sin t , t

To determine

To calculate: The curvature of the curve r(t)=2cost,2sint,t.

Explanation

Given:

The equation of curve r(t)=2cost,2sint,t.

Formula used:

The curvature of curve r(t) is,

K=T(t)r(t)

Calculation:

Consider the equation of the curve, r(t)=2cost,2sint,t.

Differentiate r(t) with respect to t,

r(t)=2sint i+2cost j+ k

Take the magnitude of r(t), That is,

r(t)=(2sint i)2+(2cost j)2+ (k)2=4sin2t+4cos2t+1=4(sin2t+cos2t)+1=5

Find the value of tangent vector,

T(t)=r(t)

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