Question

When is it necessary to use L’Hôpital’s Rule to evaluate a limit? Give examples for when it is appropriate and when it is not appropriate and justify your reasoning.

Answer 1

We can see here that L'Hôpital's Rule is suitable for evaluating limits involving indeterminate forms of fractions where differentiation is applicable.

What is L'Hôpital's Rule?

L'Hôpital's Rule is a powerful tool used to evaluate limits involving indeterminate forms, typically expressed as
`(0)/(0)` or ∞/∞. It states that under certain conditions, if the limit of a quotient of functions results in an indeterminate form, then the limit of the ratio of their derivatives will yield the same result.

L'Hôpital's Rule is appropriate to use when:

• The limit of a function approaches an indeterminate form like 0/0
• Some limits involving exponential and logarithmic functions can result in indeterminate forms.