Labware - MA35 Multivariable Calculus - Single Variable Calculus
 MA35 Labs 1 » Single Variable Calculus Contents1.1 Functions of One Variable 1.1.1 Demo Tutorial 1.1.2 Linear Functions 1.1.4 Slices 1.1.5 Level Sets & Contour Points 1.1.6 Continuity 1.4 Integration Search

Level Sets & Contour Points

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The collection of all points x in the domain of a function f for which f(x) = c is called the level set of f at level c.

In general the contour of a funcion f of one real variable will be a finite set of points in the domain.

Demos

 Contour Points This demo shows the contour points of a function f(x), colored according to the value of f(x). Points that have the same color are part of the same level set.

Exercises

• 1. Find the points in the level set for each of the following:
• f(x) = x, c = 0
• f(x) = x2 - 1, c = 0
• f(x) = sin(x), c = √2/2
• f(x) = tan(x), c = 1
• 2. Given a function f(x) with level set A at c = 0 and a function g(x) with level set B at c = 0, what is the level set of the function fg(x) (equal to f(x) * g(x)) at c = 0?