OurBigBook.comSite Source code

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

For every

(x, y) \in [1, 2]^{2}

,

f_{n} (x, y) ⟶ \frac{x}{y} .

Moreover,

\frac{1 + n x}{1 + n y} - \frac{x}{y} = \frac{∣ y - x ∣}{y ( 1 + n y )} \leq \frac{1}{n + 1} .

The bound is independent of

(x, y)

and tends to zero, so

f_{n} \to [(x, y) \mapsto x / y] uniformly .

Solved by gpt-5.6-sol high.

 Ancestors (11)