MA35 Labs

MA35 – Multivariable Calculus Labs

Number of Variables: [1] [2] [3] [n] Coordinates: Cartesian | Polar

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Contents: 2 Variables

2.1 Functions of Two Variables

2.1.1 Introduction

2.1.2 Domain, Range & Function Graphs

2.1.3 Slice Curves

2.1.4 Level Sets & Contour Lines

2.1.5 Continuity

2.1.6 Normal Vectors for Linear Function Graphs

2.2 Differentiation

2.3 More Derivatives

2.4 Integration

2.5 Vector Analysis

Continuity (Page: 1 | 2 | 3 )

According to the epsilon-delta definition, a function f of two real variables is said to be continuous at (x0,y0) if for any ε > 0 there exists a δ such that | f (x,y) – f (x0,y0) | < ε whenever | (x,y) – (x0,y0) | < δ.

Demos

Continuity

Exercises

Try using the demo to test the continuity of the following functions at several points, particularly those that you suspect to be points of discontinuity.
f (x, y) = |x| + |y|
f (x, y) = |x|/x + |y|/y
f (x, y) = x + x3 + y2 + y4
f (x, y) = sin(x) + sin(y)
f (x, y) = 2xy/(x2+y2)

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