The mathematics of limits underlies all of calculus. Limits sort of enable you to zoom in on the graph of a curve — further and further — until it becomes straight. Once it's straight, you can analyze the curve with regular-old algebra and geometry. That's the magic of calculus in a very small nutshell.

Here are some important things to remember when evaluating limits:

The limit at a hole is the height of the hole.

The limit at infinity is the height of the horizontal asymptote.

Before trying other techniques, plug in the arrow number. If the result is:

A number, you're done.

A number over zero or infinity over zero, the answer is infinity.

A number over infinity, the answer is zero.

0/0 or ∞/∞, use L'Hôpital's Rule.