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- Given a function f(x,y), the set f(x,y) = c = const is called a contour curve or level curve of f. For example, for f(x,y) = 4x2 + 3y2 the level curves f = c are ellipses if c > 0. Level curves allow to visualize functions of two variables f(x,y).
people.math.harvard.edu/~knill/teaching/summer2009/handouts/week2.pdf
A graph of the various level curves of a function is called a contour map. Example: Making a Contour Map Given the function [latex]f\,(x,\ y)=\sqrt{8+8x-4y-4x^{2}-y^{2}}[/latex], find the level curve corresponding to [latex]c=0[/latex].
Nov 16, 2022 · The level curves of the function \(z = f\left( {x,y} \right)\) are two dimensional curves we get by setting \(z = k\), where \(k\) is any number. So the equations of the level curves are \(f\left( {x,y} \right) = k\).
A level curve of a function of two variables f (x, y) f (x, y) is completely analogous to a contour line on a topographical map. Figure 4.7 (a) A topographical map of Devil’s Tower, Wyoming. Lines that are close together indicate very steep terrain.
Sep 29, 2023 · A level curve of a function \(f\) of two independent variables \(x\) and \(y\) is a curve of the form \(k = f(x,y)\text{,}\) where \(k\) is a constant. A level curve describes the set of inputs that lead to a specific output of the function.
Dec 29, 2020 · Example \(\PageIndex{3}\): Drawing Level Curves. Let \(f(x,y) = \sqrt{1-\frac{x^2}9-\frac{y^2}4}\). Find the level curves of \(f\) for \(c=0\), \(0.2\), \(0.4\), \(0.6\), \(0.8\) and \(1\). Solution. Consider first \(c=0\). The level curve for \(c=0\) is the set of all points \((x,y)\) such that \(0=\sqrt{1-\frac{x^2}9-\frac{y^2}4}\).
Oct 3, 2022 · A graph of the various level curves of a function is called a contour map. Example \(\PageIndex{4}\): Making a Contour Map Given the function \(f(x,y)=\sqrt{8+8x−4y−4x^2−y^2}\), find the level curve corresponding to \(c=0\).
Level curves. One way to collapse the graph of a scalar-valued function of two variables into a two-dimensional plot is through level curves. A level curve of a function $f(x,y)$ is the curve of points $(x,y)$ where $f(x,y)$ is some constant value.
