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  1. courses.lumenlearning.com › chapter › level-curvesLevel Curves | Calculus III - Lumen Learning

    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].

  2. tutorial.math.lamar.edu › Classes › CalcIIICalculus III - Functions of Several Variables

    Nov 16, 2022 · The level curves (or contour curves) for this surface are given by the equation are found by substituting \(z = k\). In the case of our example this is, \[k = \sqrt {{x^2} + {y^2}} \hspace{0.25in}\hspace{0.25in} \Rightarrow \hspace{0.25in}\hspace{0.25in}{x^2} + {y^2} = {k^2}\]

    • what is an example of a level curve graph that will make one graph shown1
    • what is an example of a level curve graph that will make one graph shown2
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  4. math.libretexts.org › Bookshelves › Calculus12.1: Introduction to Multivariable Functions - Mathematics ...

    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.

  5. mathinsight.org › level_setsLevel sets - Math Insight

    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.

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  7. mathinsight.org › level_set_examplesLevel set examples - Math Insight

    Example 1. Let $f(x,y) = x^2-y^2$. We will study the level curves $c=x^2-y^2$. First, look at the case $c=0$. The level curve equation $x^2-y^2=0$ factors to $(x-y)(x+y)=0$. This equation is satisfied if either $y=x$ or $y=-x$. Both these are equations for lines, so the level curve for $c=0$ is two lines.

  8. math.libretexts.org › Courses › Prince_Georges5.4: Maximum and Minimum Values - Mathematics LibreTexts

    Aug 2, 2022 · We can find the maximum and minimum of \(f(x,y)\) on this curve by converting \(f(x,y)\) into a function of one variable (on the curve) and using the standard function of one variable techniques. This is best explained by some examples.

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  10. math.libretexts.org › Courses › Monroe_Community13.1: Functions of Multiple Variables - Mathematics LibreTexts

    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 \(c=0\).