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Parametric & Rectangular Equations, Slope & Concavity

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I am in a fast-paced Calculus course where I must learn new concepts each week; I find it challenging to grasp the concepts while remaining on-pace and I am experiencing great difficulty. I am really finding it difficult to grasp the concept of Parametric & Rectangular Equations, Slope & Concavity, and Tangent Lines.

Specifically, I need your help in understanding:
1. Finding the slope and concavity of given parameters.
2. Finding the equations of tangent lines.
3. Creating curves for parametric equations.

My school has been unable to provide me with a suitable tutor; I've also attempted to obtain my own outside of the school.

I would appreciate your assistance on the attachment; I would also appreciate any points you can provide to help me understand the concepts more clearly. I really want to understand the material, so your explanations are vital; please.

Thank you.

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Solution Summary

The expert examines parametric and rectangular equations and slope and concavity. Curves of parametric equations are analyzed.

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See attached. I tried to show most of my work but it was many problems so it took ...

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