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- Lines that are close together indicate very steep terrain.
courses.lumenlearning.com/calculus3/chapter/level-curves/
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.
- What does it mean for a level curve to be closed or open?
In particular a closed curve is bounded. A level curve...
- What does it mean for a level curve to be closed or open?
Apr 7, 2020 · In particular a closed curve is bounded. A level curve $f(x,y) = c$ of a smooth, nowhere constant function, if it is bounded, typically consists of one or more closed curves. A sufficient condition for $f(x,y) = c$ to be bounded is that $|f(x,y)| \to \infty$ as $|x| + |y| \to \infty$ .
Definition. Given a function f (x, y) f (x, y) and a number c c in the range of f f, a level curve of a function of two variables for the value c c is defined to be the set of points satisfying the equation f (x, y) =c f (x, y) = c.
The distance between adjacent curves near a point provides useful information about the rate of change of the function near that point. Curves that are close together mean the function changes rapidly in that region of the plane. Sketching graphs or level curves by hand both require a lot of practice.
Contour Maps and Level Curves Contour Maps: A contour map is a collection of level curves. To visualize the graph of f from the contour map, imagine raising each level curve to the indicated height. The surface is steep where the level curves are close together and it is flatter where they are farther apart.
Together they usually constitute a curve or a set of curves called the contour or level curve for that value. In principle, there is a contour through every point.
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(curves close together $=$ function changes rapidly) An advantage of level curves, compared to graphs, is that one often has to be a good artist to draw an accurate picture of the graph of a function, whereas drawing level curves requires no artistic talent.
