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You can infer all sorts of data from level curves, depending on your function. The spacing between level curves is a good way to estimate gradients: level curves that are close together represent areas of steeper descent/ascent. If the function is a bivariate probability distribution, level curves can give you an estimate of variance.
The level curve corresponding to c = 2 c = 2 is described by the equation. √9−x2 −y2 = 2 9 − x 2 − y 2 = 2. To simplify, square both sides of this equation: 9−x2 −y2 = 4 9 − x 2 − y 2 = 4. Now, multiply both sides of the equation by −1 − 1 and add 9 9 to each side: x2 +y2 = 5 x 2 + y 2 = 5.
Level Curves and Contour Plots. Level curves and contour plots are another way of visualizing functions of two variables. If you have seen a topographic map then you have seen a contour plot. Example: To illustrate this we first draw the graph of z = x2 + y2. On this graph we draw contours, which are curves at a fixed height z = constant.
Feb 28, 2021 · Calculus 3 video that explains level curves of functions of two variables and how to construct a contour map with level curves. We begin by introducing a ty...
- 21 min
- 22K
- Houston Math Prep
A level curve is just a 2D plot of the curve f (x, y) = k, for some constant value k. Thus by plotting a series of these we can get a 2D picture of what the three-dimensional surface looks like. In the following, we demonstrate this. This is essentially an animation that you can go through step by step. As you click through, you'll see a little ...
We discuss level curves: what are they, how do you find them, and what do they look like?
- 12 min
- 18.4K
- Catherine Schmurr
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Clip: Level Curves and Contour Plots. The following images show the chalkboard contents from these video excerpts. Click each image to enlarge. Reading and Examples. Level Curves and Contour Plots (PDF) Recitation Video Level Curves
