Question

Examples of l'hopital's rule not being able to be applied

Answer 1

L'Hopital's rule cannot be applied in certain cases such as when the limit is not of an indeterminate form, involves oscillation, or logarithmic functions.

Step-by-step explanation:

L'Hopital's rule is a mathematical technique used to evaluate limits when applying the direct substitution method results in an indeterminate form, such as 0/0 or ∞/∞. However, there are certain cases where L'Hopital's rule cannot be applied:

1. If the limit is not of an indeterminate form.
2. If the limit involves oscillation.
3. If the limit involves logarithmic functions.

For example, consider the limit lim(x → 0) of (sin x)/x. L'Hopital's rule cannot be used here because the limit evaluates to 0/0, which is an indeterminate form but does not fulfill the conditions for the rule to be applied. Instead, trigonometric properties need to be used to solve this limit.