Ohio Assessments for Educators (OAE) Mathematics Practice Exam

When applying L'Hôpital's Rule, what is the next step after identifying the 0/0 form?

1. Multiply by the conjugate

2. Take the derivative of the numerator and denominator

3. Substitute values directly

4. Factor the expression

The correct answer is: Take the derivative of the numerator and denominator

In the context of applying L'Hôpital's Rule, once you've identified a limit that results in a 0/0 indeterminate form, the next appropriate step is to take the derivative of both the numerator and the denominator. This process involves differentiating the top expression (the numerator) and the bottom expression (the denominator) separately, and then you can re-evaluate the limit with the new expressions. This is a powerful method because it allows you to resolve indeterminate forms and find the limit more easily. After differentiation, if the new limit still results in an indeterminate form, you can apply L'Hôpital's Rule again by differentiating once more. Other methods mentioned, like multiplying by the conjugate or factoring the expression, may also resolve limits but are not the prescribed steps after identifying a 0/0 form when using L'Hôpital's Rule. Direct substitution can often lead back to the same indeterminate form, which is why the process of taking derivatives is crucial in this specific method.