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If the function is a bivariate probability distribution, level curves can give you an estimate of variance. If the function is a classification boundary in a data-mining application, level curves can define the classification boundary between inclusion and exclusion. Level curves can show you boundaries of constant flux in some types of flow ...
Nov 26, 2019 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Mar 2, 2022 · Let us use the function f(x, y) =x3 + 5x2 + xy2 − 5y2 f (x, y) = x 3 + 5 x 2 + x y 2 − 5 y 2 and check wether it has critical points using level curves. In the first step, let us draw the level curves (blue) and the derivatives ∂f ∂x ∂ f ∂ x and ∂f ∂y ∂ f ∂ y (green). Intersections of both green curves are critical points ...
For your first question: We say a vector v ∈ Rn is perpendicular to S ⊂ Rn at p ∈ S if for every curve γ: (− a, a) → Rn s.t Img(γ) ⊂ S and γ(0) = p, it holds that γ ′ (0) ⋅ v = 0. With this definition: Suppose that f(p) ≠ 0. Let γ: (− a, a) → L(f(p)) with γ(0) = p. Notice that ∀x ∈ L(f(p)) f(x) = f(p) is constant.
Oct 10, 2015 · We can use the partial derivatives of f f to write a linear approximation of f f near some point on the level curve, (a, b) (a, b). This linear approximation would be: L(i, s) = f(a, b) + [fx(a, b)](i − a) + [fy(a, b)](s − b) L (i, s) = f (a, b) + [f x (a, b)] (i − a) + [f y (a, b)] (s − b) This linear approximation is very good very ...
Apr 15, 2012 · where C C is a constant. This isn't of types (1), (2), or (3) listed above, but we can make it of type (1) by solving the equation for y y. This gives. y = eC x. y = e C x. Then the level curves look the graphs of this equation for different values of C C. This is a family of hyperbolas with asymptotes along the x x and y y axes.
Sep 3, 2018 · You can't find the tangent line of a function, what you want is the tangent line of a level curve of that function (at a particular point). $\endgroup$ – Hans Lundmark Commented Sep 3, 2018 at 5:49
Aug 3, 2018 · Think about this geometrically. If you think about graphing these curves, or if you recognize the parametric equations for a circle, you realize that both your level curves are circles centered at the point $(1, -1)$.
Oct 11, 2018 · And I need to compute/sketch the level curves for exp(-1), exp(-1/4) and 1. I'm not sure how to go about this, I'm not even sure what the range is so this is a bit daunting. Any guidance will be greatly appreciated, Cheers :)
Apr 7, 2020 · 0. A closed curve is by definition a continuous image of a circle. This is not the same meaning of closed as in "closed set". In particular a closed curve is bounded. A level curve f(x, y) = c f (x, y) = c of a smooth, nowhere constant function, if it is bounded, typically consists of one or more closed curves.
