Here's a cool little limit problem you may wish to tackle.
If is the area of the right triangle ABC, and is the area of the segment formed by chord AB and the arc of the unit circle subtended by the central angle theta.
Find
Area of triangle:
Area of circular segment is given by . Our radius = 1.
Therefore, we have:
You can use L'Hopital:
identity:
L'Hopital again:
L'Hopital again:
Of course, you can manipulate it without L'Hopital. Whatever you want to do.