 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ia/paper-1/10e/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

f

a

when there is a real number

L

such that

lim_{h \to 0} \frac{f ( a + h ) - f ( a ) - L h}{h} = 0.

Equivalently, the difference quotient has a finite limit, and

f^{'} (a) = L = h \to 0 lim \frac{f ( a + h ) - f ( a )}{h} .

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