Continuity at a Point

HELP
Example
Does the limit exist at `x = 2`?
Is the function defined at `x = 2`?
Is the function continuous at `x = 2`?
The example functions in this applet all have something interesting going on at `x = 2`. You must decide whether or not the function is continuous at `x = 2`. Recall:
The function `f` is continuous at the `x`-value `c` if
  1. `lim_(x-->c) f(x) = L` where `L` is a real number
    (so `L` can't be `oo` or `-oo`), and
  2. `f(c) = L`.
Informally, we say the function is continuous at a point if the limit exists, the function value exists, and they are equal to each other.

Explore

  1. Go through the examples listed below the applet, and see if you can answer the questions correctly before you click the "Check" button!