 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ii/paper-1/26i/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

X \subseteq R^{N}

and

p \in X

T_{p} X = {γ^{'} (0) : γ : (- ε, ε) \to X is smooth and γ (0) = p} .

Equivalently, in a local parametrization

φ : U \subseteq R^{d} \to X

with

φ (u) = p

, one has

T_{p} X = im D φ_{u}

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