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a) A curve can be parametrized by calculating its intersection point with the line y = tx, in which case the parameter is the slope t of the intersecting line. Using this idea, form the parametrization of the curve x= t - t³, y=t² = t4,t E R. b) Determine the y-coordinate of the highest point of the curve by first deducing the r' (t) is horizontal". corresponding parameter value(s) from the condition "tangent vector c) Form an integral expression for the arc length of one loop and calculate its approximation using a program.

a) A curve can be parametrized by calculating its intersection point with the line y = tx, in which case the parameter is the slope t of the intersecting line. Using this idea, form the parametrization of the curve x= t - t³, y=t² = t4,t E R. b) Determine the y-coordinate of the highest point of the curve by first deducing the r' (t) is horizontal". corresponding parameter value(s) from the condition "tangent vector c) Form an integral expression for the arc length of one loop and calculate its approximation using a program.

Elementary Geometry for College Students
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter10: Analytic Geometry
Section10.CT: Test
Problem 22CT
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Implicit plane curve g(x, y) = x² + y³ - x²y = 0 represents a patterned "butterfly". a) A curve can be parametrized by calculating its intersection point with the line y = tx, in which case the parameter is the slope t of the intersecting line. Using this idea, form the parametrization of the curve x = t t³, y = t²t, t E R. b) Determine the y-coordinate of the highest point of the curve by first deducing the r' (t) - corresponding parameter value(s) from the condition "tangent vector c) Form an integral expression for the arc length of one loop and calculate its approximation using a program. 0.2- y 0.1- f -0.1 0.1 0.2 0.3 X -0.1 -0.2- -0.3 -0.2 is horizontal".
Transcribed Image Text:Implicit plane curve g(x, y) = x² + y³ - x²y = 0 represents a patterned "butterfly". a) A curve can be parametrized by calculating its intersection point with the line y = tx, in which case the parameter is the slope t of the intersecting line. Using this idea, form the parametrization of the curve x = t t³, y = t²t, t E R. b) Determine the y-coordinate of the highest point of the curve by first deducing the r' (t) - corresponding parameter value(s) from the condition "tangent vector c) Form an integral expression for the arc length of one loop and calculate its approximation using a program. 0.2- y 0.1- f -0.1 0.1 0.2 0.3 X -0.1 -0.2- -0.3 -0.2 is horizontal".
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