Calculus for Scientists and Engineers Early Transcendental Level curves of planes Prove that the level curves of the plane a x b y c z = d are parallel lines in the x y plane, provided a 2 b 2 ≠ 0 and c ≠ 0 Functions of Several Variables Graphs and Level CurvesExample 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 cLevel Curves and Surfaces Example 3 In mathematics, a level set of a function f is a set of points whose images under f form a level surface, ie a surface such that every tangent plane to the surface at a point of the set is parallel to the level set
How Do You Sketch Level Curves Of Multivariable Functions Krista King Math Online Math Tutor
