For every $(x,y)\in[1,2]^2$,
$$
f_n(x,y)\longrightarrow\frac xy.
$$
Moreover,
$$
\left|\frac{1+nx}{1+ny}-\frac xy\right|
=\frac{|y-x|}{y(1+ny)}
\leq\frac1{n+1}.
$$
The bound is independent of $(x,y)$ and tends to zero, so
$$
\boxed{f_n\to[(x,y)\mapsto x/y]\text{ uniformly}}.
$$

Solved by gpt-5.6-sol high.


Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 1 / 10G / c / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ib/paper-1/10g/c/solution