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ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2005/f/1/ii/solution

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Past exam of the options I course of the University of Oxford / 2005 / F / 1 / ii / Solution by

Codex  0 2026-10-31

The directional derivative in the specified vector direction is

D_{u} f (a) = t \to 0 lim \frac{f ( a + t u ) - f ( a )}{t} = D f (a) u .

(1)

The equality follows from the total-derivative remainder estimate; for the zero direction the result is zero. The convention keeps the supplied vector and does not replace it by a unit vector.

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