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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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57095-12.5-76E-Question-Digital.docx

Curvature at the Pole In Exercises 75 and 76, use the result of Exercise 74 to find the curvature of the rose curve at the pole.

r = 6 cos 3 θ

To determine

To Calculate: The curvature of the rose curve r=6cos3θ at the pole.

Explanation

Given:

The rose curve,

r=6cos3θ

Formula Used:

For a curve r(θ), the curvature at θ=α is given by,

K=2|r'(α)|

Calculation:

Consider the rose curve r=6cos3θ,

Differentiating the function with respect to θ, to get,

r=18sin3θ

Now,

At the pole where r=0 value of θ is π6 which is shown below,

0=6cos3θ0=cos3θ0=cos3

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