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12.1 Parametric Equations

12.1 Parametric Equations. Math 6B Calculus II. Parametrizations and Plane Curves. Path traced by a particle moving alone the xy plane. Sometimes the graph cannot be expressed as a function of x or y . Definition. If x and y are continuous functions x = f ( t ) , y = g ( t )

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12.1 Parametric Equations

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  1. 12.1 Parametric Equations Math 6B Calculus II

  2. Parametrizations and Plane Curves • Path traced by a particle moving alone the xy plane. Sometimes the graph cannot be expressed as a function of x or y.

  3. Definition • If x and y are continuous functions x = f (t) , y = g(t) over an interval of t – values , then the set of points (x , y) = ( f (t) , g(t)) defined by these equations is a curvein the coordinate plane.

  4. Definition • The equations are parametric equations. The variable t is a parameter for the curve and its domain I is the parameter interval. If I is a closed interval, , the pt. ( f (a) , g(a)) is the initial point of the curve and ( f (b) , g(b)) is called the terminal point of the curve.

  5. Definition • When we give parametric equations and a parameter interval for a curve in the plane, we say that we have parameterized the curve. The equations and interval constitute a parameterization of the curve.

  6. Tangents • To find the slope of the tangent dy/dx from the parametric equations x = f (t) and y = g (t), let us use the chain rule of dy/dt

  7. Tangents • We can get dy/dx by itself and therefore get the slope of the tangent line.

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