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Let a > 0 and let f: [0, a] –→ R be an increasing continuous function. Consider the curve C parametrized by cos(f(x)) dr, / sin(f(x)) dæ a) Show that C is parametrized by arc length. b) Determine the curvature k(s) of C. c) Use b) to find a parametrization of the curve whose curvature is given by K(s) = s, with s > 0.

Let a > 0 and let f: [0, a] –→ R be an increasing continuous function. Consider the curve C parametrized by cos(f(x)) dr, / sin(f(x)) dæ a) Show that C is parametrized by arc length. b) Determine the curvature k(s) of C. c) Use b) to find a parametrization of the curve whose curvature is given by K(s) = s, with s > 0.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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Let a > 0 and let f: [0, a] –→ R be an increasing continuous function. Consider the curve C parametrized by cos(f(x)) dr, sin(F (2)) da a) Show that C is parametrized by arc length. b) Determine the curvature k(s) of C. c) Use b) to find a parametrization of the curve whose curvature is given by K(s) = s, with s > 0.
Transcribed Image Text:Let a > 0 and let f: [0, a] –→ R be an increasing continuous function. Consider the curve C parametrized by cos(f(x)) dr, sin(F (2)) da a) Show that C is parametrized by arc length. b) Determine the curvature k(s) of C. c) Use b) to find a parametrization of the curve whose curvature is given by K(s) = s, with s > 0.
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