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Find the equation of the tangent line to the curve at the given point using implicit differentiation. Cardioid: (x2 + y2 + y)² = x² + y² at (1, 0)

Find the equation of the tangent line to the curve at the given point using implicit differentiation. Cardioid: (x2 + y2 + y)² = x² + y² at (1, 0)

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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Question
Find the equation of the tangent line to the curve at the given point using implicit differentiation. Cardioid: (x2 + y2+ y)² = x² + y² at (1, 0) y The xy-coordinate plane is given. The curve starts at the point (1, 0), goes up and left becoming less steep, changes direction at the approximate point (0.4, 0.2), goes down and left becoming more steep, passes through the origin, sharply changes direction at the origin, goes up and left becoming less, steep, changes direction at the goes down and left becoming more steep, crosses the x-axis at the point (-1, 0), changes direction at the approximate point (-1.3, -0.7), goes down and right becoming less steep, changes direction at the approximate point (0, -2), goes up and right becoming more steep, changes direction at the approximate point (1.3, -0.7), goes up and left becoming less steep, and stops at the point (1, 0). oproximate point (-0.4, 0.2),
Transcribed Image Text:Find the equation of the tangent line to the curve at the given point using implicit differentiation. Cardioid: (x2 + y2+ y)² = x² + y² at (1, 0) y The xy-coordinate plane is given. The curve starts at the point (1, 0), goes up and left becoming less steep, changes direction at the approximate point (0.4, 0.2), goes down and left becoming more steep, passes through the origin, sharply changes direction at the origin, goes up and left becoming less, steep, changes direction at the goes down and left becoming more steep, crosses the x-axis at the point (-1, 0), changes direction at the approximate point (-1.3, -0.7), goes down and right becoming less steep, changes direction at the approximate point (0, -2), goes up and right becoming more steep, changes direction at the approximate point (1.3, -0.7), goes up and left becoming less steep, and stops at the point (1, 0). oproximate point (-0.4, 0.2),
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