Limits of functions.

In this section we use the following notation:

- A neighborhood of is a subset of which contains an open interval of the form . For example, is a neighborhood of the point 1, as it contains the interval , and is a neighborhood of all of its points
- A neighborhood of is an interval of the form . For example, is a neighborhood of , and too.
- A neighborhood of is an interval of the form .For example, is a neighborhood of , and too.

A pointed neighborhood (or punctured neighborhood) of a real number is a subset of of the form , where is a neighborhood of in . For example, is a punctured neighborhood of 0.

- The general definition.

- One-sided limit at one point.
- Limits of functions and convergent sequences.
- The algebra of limits.
- Algebraic operations.
- Numerator and denominator have both a limit equal to 0 at the given point.
- Numerator and denominator have both an infinite limit at the given point.
- Difference of two functions whose limit at some point is positive infinite.
- Product of two functions with respectively an infinite limit and a limit equal to 0 at some point.

- Powers.

- Algebraic operations.
- A short catalogue.
- Polynomial functions and rational functions.
- Trigonometric functions.
- Difference two square roots.
- Logarithms and exponentials.

- The sandwich theorem.
- Vertical asymptotes.
- Other asymptotes.
- Generalizations.