3. Verify that as $n$ varies, all these functions respect conditions a), b) and c). Let $A(n)$ and $B(n)$ be the areas of the coloured parts of the tiles obtained from such functions $a_n$ and $b_n$, calculate $\lim_{n \rightarrow +\infty} A(n)$ and $\lim_{n \rightarrow +\infty} B(n)$ and interpret the results in geometric terms. The customer decides to order 5,000 tiles with the design derived from $a_2(x)$ and 5,000 with the one derived from $b_2(x)$. The painting is carried out by a mechanical arm that, after depositing the colour, returns to the initial position by flying over the tile along the diagonal. Due to a malfunction, during the production of the 10,000 tiles there is a 20\% probability that the mechanical arm drops a drop of colour at a random point along the diagonal, thus staining the newly produced tile.
3. Verify that as $n$ varies, all these functions respect conditions a), b) and c). Let $A(n)$ and $B(n)$ be the areas of the coloured parts of the tiles obtained from such functions $a_n$ and $b_n$, calculate $\lim_{n \rightarrow +\infty} A(n)$ and $\lim_{n \rightarrow +\infty} B(n)$ and interpret the results in geometric terms.
The customer decides to order 5,000 tiles with the design derived from $a_2(x)$ and 5,000 with the one derived from $b_2(x)$. The painting is carried out by a mechanical arm that, after depositing the colour, returns to the initial position by flying over the tile along the diagonal. Due to a malfunction, during the production of the 10,000 tiles there is a 20\% probability that the mechanical arm drops a drop of colour at a random point along the diagonal, thus staining the newly produced tile.