Symbolically recalculate the theorem about area ratio

Again I need help dealing with symbolic arithmetic in MC14. In the German mathematical school magazine "Alpha", issue 2/1993, I found reference to a strange sentence. In the limit towards 0 it concerns the ratio of the area of a curve segment to the area of a connected tangent triangle. Proving this theorem for special curves whose functional equation is known is not difficult. But the theorem applies to arbitrary, often continuously differentiable, curves. The associated proof in the original work involves a lot of writing work. I would like to understand this using the symbolic calculation in MC14. I have attached a “test file” for this purpose. Unfortunately my calculation fails because of the MC message that terms are becoming too large. Maybe I made mistakes too. But the calculation method is easy to describe. I ask you to check whether MC14 can do the calculations symbolically.

Kind regards, Alfred Flaßhaar