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A motion is defined by the following parametric equations. x = -sin(t), y = 2cos(t), -πst≤ π (a) Show that the particle passes through the point (1/1/2₁ √2) . Find the time t at which the particle passes through this point. (b) Find the slope of the tangent line to the curve (the orbit) at this point. d²y dx² (c) By using determine whether the orbit is concave up or concave down near this point.

A motion is defined by the following parametric equations. x = -sin(t), y = 2cos(t), -πst≤ π (a) Show that the particle passes through the point (1/1/2₁ √2) . Find the time t at which the particle passes through this point. (b) Find the slope of the tangent line to the curve (the orbit) at this point. d²y dx² (c) By using determine whether the orbit is concave up or concave down near this point.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A motion is defined by the following parametric equations. x = -sin(t), y = 2cos(t), -π≤t≤ π d²y dx² (a) Show that the particle passes through the point (b) Find the slope of the tangent line to the curve (the orbit) at this point. (c) By using (√2/2₁ √₂) . Find the time t at which the particle passes through this point. determine whether the orbit is concave up or concave down near this point. (d) At what speed does the particle go through this point? (e) Sketch the orbit and indicate the direction of the motion.
Transcribed Image Text:A motion is defined by the following parametric equations. x = -sin(t), y = 2cos(t), -π≤t≤ π d²y dx² (a) Show that the particle passes through the point (b) Find the slope of the tangent line to the curve (the orbit) at this point. (c) By using (√2/2₁ √₂) . Find the time t at which the particle passes through this point. determine whether the orbit is concave up or concave down near this point. (d) At what speed does the particle go through this point? (e) Sketch the orbit and indicate the direction of the motion.
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