In the video on the lim_0 sin(teta)/teta, the relation sin(teta) <= teta can be proved by comparison of lengths, but for the relation teta <= tan(teta) the comparison of lengths is not clear. In this case the comparison of areas is better. We can compare the area of the circular setor with the area of the triangle with the radius as base and the tangent as hight. For the first relation we can use comparison of areas as well.