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Problem of the Week: Consider the parametrized curve (cos t, sin³ t, 0), 0 < t < 27. This curve traces out a shape called an astroid, which has equation |x|2/3+|y|2/3 = 1, and which I have drawn here on Geogebra for you to look at: https://www.geogebra.org/calculator/ cvydn7gg. Your task: compute its curvature k(t). Then compute lim→0 k(t).

Problem of the Week: Consider the parametrized curve (cos t, sin³ t, 0), 0 < t < 27. This curve traces out a shape called an astroid, which has equation |x|2/3+|y|2/3 = 1, and which I have drawn here on Geogebra for you to look at: https://www.geogebra.org/calculator/ cvydn7gg. Your task: compute its curvature k(t). Then compute lim→0 k(t).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 60E
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Problem of the Week: Consider the parametrized curve (cos t, sin³ t, 0), 0 < t < 2n. This curve traces out a shape called an astroid, which has equation |x|2/3+|y|2/3 = 1, and which I have drawn here on Geogebra for you to look at: https://www.geogebra.org/calculator/ cvydn7gg. Your task: compute its curvature k(t). Then compute lim→0 k(t).
Transcribed Image Text:Problem of the Week: Consider the parametrized curve (cos t, sin³ t, 0), 0 < t < 2n. This curve traces out a shape called an astroid, which has equation |x|2/3+|y|2/3 = 1, and which I have drawn here on Geogebra for you to look at: https://www.geogebra.org/calculator/ cvydn7gg. Your task: compute its curvature k(t). Then compute lim→0 k(t).
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