<p>^ You’re allowed to use it on the AP Calculus AB exam, but no AB exam question requires its usage.</p>
<p>^^ Actually, the value of that limit is derived from the Squeeze Theorem, if you really want to find it algebraically.</p>
<p>The proof that d/dx[sin x] = cos x explicitly relies on you knowing this particular facet. (See [Derivative</a> of the Sine Function](<a href=“Oregon State University”>Oregon State University) for an example of this.) The problem is, if you use L’Hopital’s Rule to prove that lim x -> 0 sin x / x = 1, then you need to know the derivative of sin x to find that. In order to find the derivative of sin x, you need to know the limit. So one of those has to be able to come first. :)</p>
<p>And to be fair, the AP Exam doesn’t ask questions that require you to have that limit memorized on the AB exam.</p>