PARAMETRIC FUNCTIONS Today we will learn about parametric functions in the plane and analyze them using derivatives and integrals.

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Presentation transcript:

PARAMETRIC FUNCTIONS Today we will learn about parametric functions in the plane and analyze them using derivatives and integrals.

PARAMETRIC CURVES Instead of defining the points (x, y) on a planar curve by relating y directly to x, we can define both coordinates as functions of a parameter t. The resulting set of points may or may not define y as a function of x (that is, the parametric curve might fail the vertical line test). Some examples appear below:

CONVERTING PARAMETRIC EQUATIONS

PARAMETRIC DIFFERENTIATION

ANALYZING A PARAMETRIC CURVE

ARC LENGTH

ASSIGNMENT: p. 535: 1, 4, 10, 11