WebDec 25, 2024 · On the upper hemisphere of the unit sphere S 2 we have the coordinate map ϕ = ( u, v), where u ( a, b, c) = a, v ( a, b, c) = b. Let i: S 2 → R 3 be the inclusion, and i ∗ it's differential. Calculate: i ∗ ( ∂ ∂ u), i ∗ ( ∂ ∂ v) in terms of ∂ ∂ x, ∂ ∂ y, ∂ ∂ z, where x,y,z are the standard coordinates. I've fiddled ... WebJan 27, 2024 · The principle of inclusion and exclusion works for any number of events: P ( A ∪ B ∪ C) = P ( A) + P ( B) + P ( C) − P ( A ∩ B) − P ( A ∩ C) − P ( B ∩ C) + P ( A ∩ B ∩ C) $. …
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