Let [a, b] be a nondegenerate, closed, bounded interval. a) Prove that given any polynomial P on
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a) Prove that given any polynomial P on R and any ε > 0, there is a polynomial Q on R, with rational coefficients, such that P(x) - Q(x)\ < ε for all x ∈ [a, b].
b) Prove that the space C[a, b] (see Example 10.6) is separable.
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a Suppose Px a n x n a 1 x a 0 is a polynomial on R and 0 Let M supx k x a b ...View the full answer
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