For every $\varepsilon > 0$, is there a polynomial of $x^4$ without constant term, i.e., $p(x^4) = a_1 x^4 + a_2 x^8 + \cdots a_n x^{4n}$, such that $$\|p(x^4)x^2 - x\| < \varepsilon $$ for every $x \in [0,1]$?
Approximating $1/x$ by a polynomial on $[0,1]$
heller
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