![]() ![]() ![]() Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. 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: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses theĬreative Commons Attribution-NonCommercial-ShareAlike License Consider the plane curve defined by the parametric equations Try the given examples, or type in your own problem and check your answer with the step-by-step. Example 1 Determine the surface given by the parametric representation Solution Let’s first write down the parametric equations. There are really nothing more than the components of the parametric representation explicitly written down. Try the free Mathway calculator and problem solver below to practice various math topics. We will sometimes need to write the parametric equations for a surface. We start by asking how to calculate the slope of a line tangent to a parametric curve at a point. Area under a parametric curve Differentiation (1) - Parametric Equations (C4 Maths A-Level) Find the gradient function by differentiating parametric equations. 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. 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.7.2.2 Find the area under a parametric curve.7.2.1 Determine derivatives and equations of tangents for parametric curves.
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