Final answer:
The term that defines intruding or advancing gradually beyond usual or acceptable limits is 'encroach'. It implies an infringement upon space or boundaries, making 'encroach' the correct answer from the given options.
Step-by-step explanation:
To intrude or advance gradually beyond usual or acceptable limits can be best defined by the verb encroach. The word encroach directly aligns with the concept of an entity, whether it be a person, a group, or sometimes an idea, infringing upon or intruding into a space or domain it does not belong to, slowly exceeding the established boundaries. Other options provided, such as 'efficacious', relate to the effectiveness of something; 'evanescent' describes something that is fleeting or temporary, and 'exemplary' means being worthy of imitation, commendable; none of these terms specifically apply to the concept of intruding beyond limits. Therefore, A. encroach is the correct answer.