 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-2/19/a/i/solution

f

x_{0}

\forall ε > 0 \exists δ > 0 \forall x \in R : ∣ x - x_{0} ∣ < δ ⟹ ∣ f (x) - f (x_{0}) ∣ < ε .

The choice of

δ

may depend on

ε

and

x_{0}

, but must work for every

x

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