In which type of essay woild it be inappropriate to include your personal opinions

the verbal in this sentence is an infinitive. when you want to know the reason of an action, you simply ask the question "why? ". once you know the reason you can answer with "because".

many times we don´t use the word "because" but we can use another expression and that is an "infinitive of purpose". example:

-why did your brother bring a book?

-he brought a book to study.

in the answer above you can see an example of an infinitive sentence, just like in the example of your text. "he couldn´t run fast enough to beat his older sister". so, the answer is infinitive.