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Learn how to find level curves of a function in Calculus 3.
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- The Math Sorcerer
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].
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Nov 16, 2022 · So the equations of the level curves are \(f\left( {x,y} \right) = k\). Note that sometimes the equation will be in the form \(f\left( {x,y,z} \right) = 0\) and in these cases the equations of the level curves are \(f\left( {x,y,k} \right) = 0\). You’ve probably seen level curves (or contour curves, whatever you want to call them) before.
15.5.4 The Gradient and Level Curves T h e o r e m 1 5 . 1 1 s t a t e s t h a t i n a n y d i r e c t i o n o r t h o g o n a l t o t h e g r a d i e n t ∇ f ( a , b )
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Nov 10, 2020 · Exercise \(\PageIndex{4}\) For the function \(f(x,y)=x^2−2xy+5y^2+3x−2y+3\), find the tangent to the level curve at point \((1,1)\). Draw the graph of the level curve corresponding to \(f(x,y)=8\) and draw \(\vecs ∇f(1,1)\) and a tangent vector. Hint. Calculate the gradient at point \((1,1)\). Answer
