Calculus 6.08f - The Small Angle Theorem

Using l'Hopital's Rule to prove the Small Angle Theorem
The limit as x approaches zero of (sin x) / x = 1

[@ahnafkhan8115]

Instead of using L'Hopital's rule, can we not take values very close to 0 and substitute for x?

[@derekowens]

Yes, you can use nearby values. The idea, though, is that doing so will result in an *approximation*, not the exact value of the limit. The smaller the interval used, the closer the approximation will be. But you can never be *exact* with that method because you can not shrink the interval all the way to zero. The calculus techniques give us a way to find the exact value.

[@ahnafkhan8115]

Thanks for this detailed answer!