Define A a0 a2x2 a2nx2n the family of polynomials cont

Define A_+ = {a_0 + a_2x^2 + ... + a_2nx^2n} - the family of polynomials containing only even powers of x. Similarly. A_= {a_1x + a_3x^3 + ... + a_2n +|1x^2n+l} is the collection of polynomials containing only odd powers of x.

(a) The sets A₊ consisting of even powers of x is dense in C[0,1] as the sum of the reciprocals of even positive integers diverges . So Muntz theorem applies in this situation.

(b) The closue wont contain the constant functions.So not true.

$Define A_+ = {a_0 + a_2x^2 + ... + a_2nx^2n} - the family of polynomials containing only even powers of x. Similarly. A_= {a_1x + a_3x^3 + ... + a_2n +|1x^2n+l$

Define A a0 a2x2 a2nx2n the family of polynomials cont

Solution

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