Search results
- 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.
people.math.harvard.edu/~knill/teaching/summer2009/handouts/week2.pdf
Given a function [latex]f\,(x,\ y)[/latex] and a number [latex]c[/latex] in the range of [latex]f[/latex], a level curve of a function of two variables for the value [latex]c[/latex] is defined to be the set of points satisfying the equation [latex]f\,(x,\ y)=c[/latex].
About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright ...
- 3 min
- 1140
- for myself
A level curve of the function f(x,y)=−x2−2y2=c is shown. The level curves are not restricted to the domain −2≤x≤2, −2≤y≤2, so an entire ellipse is visible for each value of c.
For some constant $c$, the level curve $f(x,y)=c$ is the graph of $c=-x^2-2y^2$. As long as $c 0$, this graph is an ellipse, as one can rewrite the equation for the level curve as \begin{align*} \frac{x^2}{-c} + \frac{y^2}{-c/2} =1.
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 \(f\left( {x,y} \right) = k\).
Given a function f (x, y) f (x, y) and a number c c in the range of f, a 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.
Dec 29, 2020 · A level curve at \(z=c\) is a curve in the \(x\)-\(y\) plane such that for all points \((x,y)\) on the curve, \(f(x,y) = c\). When drawing level curves, it is important that the \(c\) values are spaced equally apart as that gives the best insight to how quickly the "elevation'' is changing.
