We recommend using aĪuthors: Gilbert Strang, Edwin “Jed” Herman Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: Consider the teardrop shape formed by the parametric equations, x t ( t 2 1 ), y t 2 1 as seen in Example 10.3.19. If you are redistributing all or part of this book in a print format,
PARAMETRIC EQUATIONS CALCULUS EXAMPLES LICENSE
Want to cite, share, or modify this book? This book uses theĬreative Commons Attribution-NonCommercial-ShareAlike License The graph of the parametric equations, x t ( t 2 1 ), y t 2 1 crosses itself as shown in Figure. Consider the plane curve defined by the parametric equations
PARAMETRIC EQUATIONS CALCULUS EXAMPLES HOW TO
We start by asking how to calculate the slope of a line tangent to a parametric curve at a point. Furthermore, we should be able to calculate just how far that ball has traveled as a function of time. If the position of the baseball is represented by the plane curve ( x ( t ), y ( t ) ), ( x ( t ), y ( t ) ), then we should be able to use calculus to find the speed of the ball at any given time. An example of applying Calculus to a parametric curve is finding the arc length of a parametrized curve over a certain interval. For example, if we know a parameterization of a given curve, is it possible to calculate the slope of a tangent line to the curve? How about the arc length of the curve? Or the area under the curve?Īnother scenario: Suppose we would like to represent the location of a baseball after the ball leaves a pitcher’s hand. Now that we have introduced the concept of a parameterized curve, our next step is to learn how to work with this concept in the context of calculus. 7.2.4 Apply the formula for surface area to a volume generated by a parametric curve.7.2.3 Use the equation for arc length of a parametric curve.The portion of the plane 7x +3y +4z 15 7 x + 3 y + 4 z 15 that lies in the 1 st octant. 7.2.2 Find the area under a parametric curve. For problems 1 6 write down a set of parametric equations for the given surface.7.2.1 Determine derivatives and equations of tangents for parametric curves.
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