4/1000, do not use L'Hopital's rule for this limit! calculus 1

Added: 2026-05-17

[00:00:00]Question number four out of 1,000. Here we'll be evaluating this limit. However, we will not be using Lapito's rule. So, how do we do it? Well, we have sin x and sin x and x is approaching zero. The key is we have to use the limit as that's the theta approaching zero of sin theta over theta. This right here is equal to 1. For this limit in particular, even though it's in the zero over zero indeterminant form, you should not be using Liito's rule to prove it. You should be doing geometry for this right here. Because if you use Liito's rule, you'll run into a circular reasoning.

[00:00:40]But we can talk about that later. Right here, how do we produce this form in our limit though? Well, I really want to have sin x overx, right? So, let's go ahead and divide it by x and do the same on the bottom. That way we will see that's the limit as x approaching zero.

[00:00:59]The top is sin x overx and then that will be one and that's another sin x overx.

[00:01:08]And per discussion earlier when x approaches zero this will just give us one and likewise this will also give us one.

[00:01:19]So the top is one the bottom is 1 + 1.

[00:01:23]All in all, we get one half.

[00:01:26]That's it.