L-Hospital's Rule for Indeterminate Forms

L-Hospital's Rule should only be used when you have an indeterminate form. These are shown by the table below. The first two indeterminate forms are the most common varieties.

Source: https://math.stackexchange.com/questions/1581721/list-of-indeterminate-forms-in-mathematics

L-Hospital's Rule states that you take the derivative of the numerator and then the denominator and try to take the limit at the same value of that function. If this results in an indeterminate form, you will need to repeat the process. Here are two examples:

The second example uses L-Hospital's Rule four times because of the repeated appearance of indeterminate forms. 

Source of the two examples: https://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rule