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For a plane curve r(t) = (x(t), y(t)), k(t) : k(4) = = |x'(t)y"(t) — x"(t)y' (t)| (x'(t)² + y'(t)²)³/2 Use this equation to compute the curvature at the given point. r(t) = (2t¹, t³), t = 4.

For a plane curve r(t) = (x(t), y(t)), k(t) : k(4) = = |x'(t)y"(t) — x"(t)y' (t)| (x'(t)² + y'(t)²)³/2 Use this equation to compute the curvature at the given point. r(t) = (2t¹, t³), t = 4.

Trigonometry (MindTap Course List)
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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For a plane curve r(t) = (x(t), y(t)), k(t) : k(4) = = = |x'(t)y"(t) — x"(t)y' (t)| (x'(t)² + y'(t)²)³/2 Use this equation to compute the curvature at the given point. r(t) = (2tª, t³), t = 4.
Transcribed Image Text:For a plane curve r(t) = (x(t), y(t)), k(t) : k(4) = = = |x'(t)y"(t) — x"(t)y' (t)| (x'(t)² + y'(t)²)³/2 Use this equation to compute the curvature at the given point. r(t) = (2tª, t³), t = 4.
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