In this video I go over further into determining the slope of tangent lines to parametric curves and this time show the general condition in which we can do this. In my earlier video I derived the equation for the slope but simply assumed that for some parametric equations we can remove the parameter to form an equation of the form y = F(x). In this video I show that the general condition in which we can eliminate the parameter is if, for the parametric equations x = f(t) and y = g(t), we have f’ being a continuous function that is never equal to 0 for a given interval. This condition makes it possible to find the inverse of the function thus we can use that the fact to plug into g(t). I explain how to do this in the video so make sure to watch it!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhuMbzM5UzIft5JqRqg
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/parametric-calculus-tangents-general-condition
Related Videos:
Parametric Calculus: Tangents:
Parametric Equations and Curves:
Inverse Functions - f-1(x) - An Introduction:
Inverse Functions Part 2: One to One Functions and the Horizontal Line Test: .
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I don't always derive the tangent of parametric curves but when I do I usually use inverse functions in the proof ;)
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/parametric-calculus-tangents-general-condition
Calculus is sometimes called calculus. Although the origins of the account of integration are very ancient to pre-Greek, there is evidence that ancient Egyptians may have been aware of such knowledge as well. (See Moscow Sports Card.) Is considered with a method, which made it possible to calculate the spaces and sizes of areas and solids. Archimedes developed this method further, and invented methods that are similar to contemporary concepts.