The squeeze theorem is another method we can use to find the limit of a function. If we can show that the limit of a function at a point is always greater than or equal to some value and less than or equal to that same value, than by the squeeze theorem we can prove that the limit of the function a that point has the same value.

The precise definition of the limit (also called the epsilon-delta definition of the limit), is just a way for us to prove that a limit exists. This is one of the hardest topics in calculus, so don't get discouraged if you need to go over it multiple times!

The general limit of a function only exists when the left-hand limit exists, the right-hand limit exists, and the left- and right-hand limits are equal to one another. Even when the general limit doesn't exist because one of these conditions isn't met, the one-sided limits (the left-hand limit and/or the right-hand limit), can still exist independently.

When you have to find the limit of trigonometric functions, there are special trig limit formulas you'll want to use in order to simplify your function to a point where you can evaluate its limit.

Sometimes you'll be asked to find various limits of a function defined by a crazy graph. The trick is to understand that the limit is just the value the function approaches as you trace your finger along the graph toward the limit value. You may find that the left- and right-hand limits of a function are different at some points, and that the value of the function at a point is not always equal to the limit of the function there.

To use conjugate method to solve for the limit of a rational function, just multiply the numerator and denominator by the conjugate. This might simplify the fraction to the point where you can use substitution with the remaining function to find the limit.

To use factoring to solve for the limit of a rational function, just factor the numerator and denominator completely, then see if you can cancel common factors from the fraction. This might simplify the fraction to the point where you can use substitution with the remaining function to find the limit.

To use substitution to solve a limit problem, just plug the number you're approaching into the function. If you get a real-number answer, then the substitution worked. If not, you'll need to use a different technique to solve for the limit.

Everything you need to know about the unit circle.

The inverse of a function is its reflection over the line y=x.