Continuity Examples

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In this video I go over some very useful examples on continuity and show where and why discontinuities arise. I also go over the Greatest Integer Function in terms continuity and show that it has 'Jump' continuities.


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Continuity – Examples

Continuity Examples.jpg

Definition

A function f is continuous at a number a if:

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This definition implicitly requires that:

  1. f(a) is defined (that is, a is in the domain of f)
  2. limx→a ⁡f(x) exists
  3. limx→a⁡ f(x) = f(a) exists

We say a function is discontinuous otherwise.

Example 1

In the figure below, at which numbers is f discontinuous? Why?

image.png

Example 2

Where is each of the following functions discontinuous?

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