Question: Problem 3. Let C(R) be the vector space of all continuous functions from R to R. Prove that for all n E N, the set

Problem 3. Let C(R) be the vector space of all continuous functions from R to R. Prove that for all n E N, the set {sin(x), sin(2x), sin(22x), . .., sin(2"x) }. is a linearly independent subset of C(R). [HINT: Given a relation, try evaluating at 7/2, or at 7/2k.]

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