9.3: Calculus with Parametric Equations When a curve is defined parametrically, it is still necessary to find slopes of tangents, concavity, area, and.

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Presentation transcript:

9.3: Calculus with Parametric Equations When a curve is defined parametrically, it is still necessary to find slopes of tangents, concavity, area, and distance. These each require the use of derivatives or integrals.

Slope and Tangent Lines

Tangent Lines

Find the points on C where the tangent is horizontal or vertical.

Second Derivative

Concavity of Parametric Curves Ex. Determine where the curve C is concave upward or downward.

Area of Parametric Functions

Area of a Parametric Function

Arc Length of a Parametric Curve