Polar Coordinates: Example 12: Limaçons Analytical Proof: Part 2: Question B

In this video I go over Part 2 of Example 12 on Polar Coordinates which involves providing an analytical approach to the Limaçon curves of Example 11. In Part 2 I look at Question B which asks to prove that the Limaçon loses it’s “dimple” at c = ½. I prove this by using the Second Derivative Test to show that the dimple is simple a local maximum. Similarly I do the same for c = -1/2 and show that instead the dimple can be viewed as the local minimum. This is another very detailed proof video but once again provides an in-depth approach in breaking down polar curves, so make sure to watch this video!

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Related Videos:

Polar Coordinates: Example 12: Limaçons Analytical Proof: Part 1: Question A: https://youtu.be/90XjQVkLBVY Polar Coordinates: Example 11: Limaçons + Cochlea + Archimedean Screw: https://youtu.be/GByUVHGAMe0 Polar Coordinates: Example 10: Graphing r = sin(8ϴ/5): https://youtu.be/m-A35NDX7b0 Polar Coordinates: Graphing With Polar Curves with Desmos Calculator: https://youtu.be/xY9Be9HHRsk Polar Coordinates: Example 9: Cardioid: Part 4: https://youtu.be/R6UtQD8tUF0 Polar Coordinates: Example 9: Cardioid: Part 3: Question B: https://youtu.be/-TZHaTjHfb8 Polar Coordinates: Example 9: Cardioid: Part 2: Question A: https://youtu.be/gUYmzZ8Cfhg Polar Coordinates: Example 9: Cardioid: Part 1: Slope Formula & Trigonometric Algebra: https://youtu.be/MlIhueP36EE Polar Coordinates: Tangents to Polar Curves: https://youtu.be/DJso0gmxCBY Polar Coordinates: Symmetry: https://youtu.be/TWxforTOvxM Polar Coordinates: Example 8: Four-Leaved Rose: https://youtu.be/mTk5j0jD3dE Polar Coordinates: Example 7: Cardioid: https://youtu.be/rPErcaqNUIY Polar Coordinates: Example 6: Part 2: Polar Circle to Cartesian: https://youtu.be/biUHN-BphkE Polar Coordinates: Example 5: Straight Lines: https://youtu.be/AGSz3EVi05A Polar Coordinates: Example 4: Circle: https://youtu.be/ebsaIlXaZxs Polar Coordinates: Example 3: Cartesian to Polar Polar Coordinates: Example 2: Polar to Cartesian: https://youtu.be/mvpb9QshNNU Polar Coordinates: Cartesian Connection: https://youtu.be/HcaTYrpmGaU Polar Coordinates: Example 1: https://youtu.be/q_kpqPpoLqE Polar Coordinates: https://youtu.be/-KAdZL-N4ok Parametric Equations and Polar Coordinates: https://youtu.be/usSors49Gdw Second Derivative Test - A brief Introduction: http://youtu.be/lOwK5rQh0Kk .

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