grandes-ecoles 2021 Q33

grandes-ecoles · France · centrale-maths1__mp Sequences and Series Properties and Manipulation of Power Series or Formal Series

Let $A > 2$. Let $f$ be a continuous and bounded function from $\mathbb{R}$ to $\mathbb{R}$ and $P$ a polynomial of degree $p$. Justify that there exists a constant $K$ such that $$\forall x \in \mathbb{R} \setminus ]-A, A[, \quad |f(x) - P(x)| \leqslant K|x|^{p}.$$

Let $A > 2$. Let $f$ be a continuous and bounded function from $\mathbb{R}$ to $\mathbb{R}$ and $P$ a polynomial of degree $p$. Justify that there exists a constant $K$ such that
$$\forall x \in \mathbb{R} \setminus ]-A, A[, \quad |f(x) - P(x)| \leqslant K|x|^{p}.$$

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