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 |

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

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