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Learn how to find level curves of a function in Calculus 3.
- 13 min
- 72.7K
- The Math Sorcerer
Level curves of the function g(x,y)=√9−x2−y2 g (x y) = 9 − x 2 − y 2, using c=0,1,2 c = 0 1, 2, and 3 3 (c=3 c = 3 corresponds to the origin). A graph of the various level curves of a function is called a contour map.
Nov 16, 2022 · In this section we will give a quick review of some important topics about functions of several variables. In particular we will discuss finding the domain of a function of several variables as well as level curves, level surfaces and traces.
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 typical temperature map as an...
- 21 min
- 22K
- Houston Math Prep
Get the free "Level Curve Grapher" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha.
Jan 28, 2022 · Another good way to visualize the behaviour of a function \(f(x,y)\) is to sketch what are called its level curves. By definition, a level curve of \(f(x,y)\) is a curve whose equation is \(f(x,y)=C\text{,}\) for some constant \(C\text{.}\) It is the set of points in the \(xy\)-plane where \(f\) takes the value \(C\text{.}\)
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Jan 22, 2022 · In order to find a few level curves, I began by calculating the following for a constant c: $e^{\sqrt{x^2-y^2}}=c$, This gives $\sqrt{x^2-y^2}=\ln(c)$ and $c>0$. The first level curve, when $c=1$: $$g(x,y)=e^{\sqrt{x^2-y^2}}=1\implies x^2-y^2=0\implies y=±x,$$ which I can
