Intuitive Definition. Let y = f(x) be a function. Suppose that a and L are numbers such that
  • whenever x is close to a but not equal to a, f(x) is close to L;
  • as x gets closer and closer to a but not equal to a, f(x) gets closer and closer to L; and
  • suppose that f(x) can be made as close as we want to L by making x close to a but not equal to a.
Then we say that the limit of f(x) as x approaches a is L and we write

Examples.