Question: a) Prove that given f C[a, b], then there is a sequence of one-variable polynomials Pn such that Pn f uniformly on [a,

a) Prove that given f ∈ C[a, b], then there is a sequence of one-variable polynomials Pn such that Pn → f uniformly on [a, b] as n → ∞.
b) Prove that the metric space C[a, b] (see Example 10.6) is separable.

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