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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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BuyFindarrow_forward

Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem
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Finding CurvatureIn Exercises 29–36, find the curvature of the curve.

r ( t ) = 4 cos 2 π t i + 4 sin 2 π t j

To determine

To calculate: The curvature of the curve r(t)=4cos2π t i+4sin2π t j.

Explanation

Given:

The provided curve is, r(t)=4cos2π t i+4sin2π t j.

Formula Used:

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

Calculation:

Consider the provided curve is shown below,

r(t)=4cos2π t i+4sin2π t j

Now, differentiate r(t) and find the absolute value of r(t) as calculated below,

r(t)=8π sin2π t i+8πcos2π t j

Now, find the magnitude of r(t) as calculated below,

r(t) =64π2=8π

Apply formula of unit tangent vector and then solve

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