Answered: Find the curvature of the function…

Find the curvature of the function y=ln(3x)y=ln(3x) at x=3x=3. Find the radius of curvature at x=3x=3. If the radius is infinite, enter 'oo' for ∞∞.

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

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Question

Find the curvature of the function

y=ln(3x)y=ln(3x)

at x=3x=3.

Find the radius of curvature at x=3x=3. If the radius is infinite, enter 'oo' for ∞∞.

Find the center of curvature at x=3x=3. If the center of curvature does not exist, enter "DNE".

Hint if needed: Multiply the normal vector by the radius of curvature, and then add this vector quantity to the position vector. The components of the result will be the coordinates of the center of curvature. :)

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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