Question 1
Let $f$ be defined on $\mathbb R$. Suppose that for every real $c>0$ there is a polynomial $P_c$ with real coefficients such that
$$|f(x)-P_c(x)|\le cx^{1998}\qquad(x\in\mathbb R).$$
Prove that $f$ is a polynomial with real coefficients.
The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale.
$$|f(x)-P_c(x)|\le cx^{1998}\qquad(x\in\mathbb R).$$
Prove that $f$ is a polynomial with real coefficients.
The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale.