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Unformatted text preview: 10.1 Parametric Functions Greg Kelly, Hanford High School, Richland, Washington In chapter 1, we talked about parametric equations. Parametric equations can be used to describe motion that is not a function. ( 29 ( 29 x f t y g t = = If f and g have derivatives at t , then the parametrized curve also has a derivative at t . → The formula for finding the slope of a parametrized curve is: dy dy dt dx dx dt = This makes sense if we think about canceling dt . The formula for finding the slope of a parametrized curve is: dy dy dt dx dx dt = We assume that the denominator is not zero. → To find the second derivative of a parametrized curve, we find the derivative of the first derivative: dy dt dx dt ′ = 2 2 d y dx ( 29 d y dx ′ = 1. Find the first derivative ( dy/dx ). 2. Find the derivative of dy/dx with respect to t . 3. Divide by dx/dt . → Example 2 (page 514): 2 2 3 2 Find as a function of if and ....
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 Fall '05
 Riggs
 Equations, Derivative, Differential Calculus, Pythagorean Theorem, Parametric Equations, Vectorvalued function, Hanford High School, Greg Kelly, dx dx dt

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