Ford Huff
01/09/2024 · Elementary School
1. Majorer et minorer sur \( \mathbb{R} \) la fonction \( g: x \mapsto \frac{x^{2}}{x^{2}+1} \) 2. a. Montrer que pour tout réel \( x,|2 x| \leq x^{2}+1 \) b. Majorer et minorer sur \( \mathbb{R} \) la fonction \( \left.x \mapsto \frac{x^{2}-2 x}{x^{2}+1} \right\rvert\, \)
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1. La fonction \( g(x) = \frac{x^{2}}{x^{2}+1} \) est majorée par 1 et minorée par 0 pour tout \( x \in \mathbb{R} \).
2. a. Pour tout \( x \in \mathbb{R} \), \( |2x| \leq x^{2} + 1 \).
b. La fonction \( h(x) = \frac{x^{2} - 2x}{x^{2} + 1} \) est majorée par 1 et minorée par -1 pour tout \( x \in \mathbb{R} \).
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