Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2024 / Paper 1 / 19 / b / i / Solution

The epsilon-delta definition of continuity says that $f$ is continuous at $a$ ifHere $a$ belongs to the domain of $f$, and the implication is required for every $x$ in that domain. The number $\delta$ may depend on $\epsilon$ and $a$, but must work for all such $x$ simultaneously.