Labware - MA35 Multivariable Calculus - Two Variable Calculus

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Continuity (Page: 1 | 2 | 3 | 4 )

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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 &delta such that | f(x,y) - f(x0,y0) | < ε whenever | (x,y) - (x0,y0) | < &delta.

Demos

Exercises

  • 1. 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|
  • 2. f(x, y) = |x|/x = |y|/y
  • 3. f(x, y) = x + x3 + y2 + y4
  • 4. f(x, y) = sin(x) + sin(y)
  • 5. f(x, y) = 2xy/(x2+y2)