 Solution

ID: 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

f

is continuous at

a

for every ε > 0 there exists δ > 0 such that ∣ x - a ∣ < δ ⟹ ∣ f (x) - f (a) ∣ < ε .

Here

a

belongs to the domain of

f

, and the implication is required for every

x

in that domain. The number

δ

may depend on

ε

and

a

, but must work for all such

x

simultaneously.

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