2010-10-02, 10:57 PM
Yeah, L'Hopital makes it nice:
4 sin 4x / sin 2x => 16 cos 4x / 2 cos 2x => 16 cos 0 / 2 cos 0 = 16/2 = 8.
But there's also another way, using the sine double angle identity:
4 sin 4x / sin 2x => 4 sin 2(2x) / sin 2x => 4 (2 sin 2x cos 2x) / sin 2x => 8 cos 2x => 8 cos 0 = 8.
4 sin 4x / sin 2x => 16 cos 4x / 2 cos 2x => 16 cos 0 / 2 cos 0 = 16/2 = 8.
But there's also another way, using the sine double angle identity:
4 sin 4x / sin 2x => 4 sin 2(2x) / sin 2x => 4 (2 sin 2x cos 2x) / sin 2x => 8 cos 2x => 8 cos 0 = 8.