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Astroid is given by rectangular equation r2/3 + y2/3 = 1. In parametric form the curve is given by the equations (0) = cos³0 and y(0) = sin³ 0, 0≤ 0 ≤ 2. -1 (a) Find the point (s) where the curve is not smooth. Explain your answer. Indicate these points on the graph. (b) Find the points on the curve where tangent is horizontal or vertical. (c) Find an equation of the tangent line to the curve when 0 = π/4.

Astroid is given by rectangular equation r2/3 + y2/3 = 1. In parametric form the curve is given by the equations (0) = cos³0 and y(0) = sin³ 0, 0≤ 0 ≤ 2. -1 (a) Find the point (s) where the curve is not smooth. Explain your answer. Indicate these points on the graph. (b) Find the points on the curve where tangent is horizontal or vertical. (c) Find an equation of the tangent line to the curve when 0 = π/4.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(10) Astroid is given by rectangular equation x2/3 + y2/3 = 1. In parametric form the curve is given by the equations (0) = cos³ 0 and y(0) = sin³ 0, 0≤0 ≤ 2. -1 (a) Find the point (s) where the curve is not smooth. Explain your answer. Indicate these points on the graph. (b) Find the points on the curve where tangent is horizontal or vertical. (c) Find an equation of the tangent line to the curve when 0 = π/4. (d) Find the arc length of the curve. (e) Suppose that the top part of the curve is revolved about the x-axis. Find the surface area of the surface of revolution.
Transcribed Image Text:(10) Astroid is given by rectangular equation x2/3 + y2/3 = 1. In parametric form the curve is given by the equations (0) = cos³ 0 and y(0) = sin³ 0, 0≤0 ≤ 2. -1 (a) Find the point (s) where the curve is not smooth. Explain your answer. Indicate these points on the graph. (b) Find the points on the curve where tangent is horizontal or vertical. (c) Find an equation of the tangent line to the curve when 0 = π/4. (d) Find the arc length of the curve. (e) Suppose that the top part of the curve is revolved about the x-axis. Find the surface area of the surface of revolution.
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