Please provide thorough proof or derivation for Fundamental Theorem of Calculus Part 1 (Limit of sum...

Please provide thorough proof or derivation for Fundamental Theorem of Calculus Part 1 (Limit of sum of Areas is equal to F(b)-F(a)

Expert Solution

Colby Messinger answered 2 years ago

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please provide explanations within your proof 1) Prove that if ?1, ?2 are subspaces of ? such that ?1 + ?2 = ?1 ⊕ ?2 then there is a linear isomorphism ? : ?1 × ?2 → ?1 ⊕ ?2. (Recall: Given two sets ?1, ?2 the cross product ?1 × ?2 is the set of elements (?, ?) where ? ∈ ?1 and ? ∈ ?2 with pointwise addition and scalar multiplication.) 2) Let ? be a finite dimensional...

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