EDB — 20Y

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Esercizio 26

[20Y](Proposto il 2022-12) Calcolate estremo superiore e inferiore dei seguenti insiemi (dove \(n,m\) sono interi).

\begin{eqnarray*} \left\{ \frac{mn}{m^ 2+n^ 2}: n,m≥ 1 \right\} \quad ,\quad \left\{ \frac{mn}{m+n}: n,m≥ 1 \right\} \\ \left\{ 2^ n+2^ m : n,m∈ℕ \right\} \quad ,\quad \left\{ 2^ n+2^ m: n,m∈ℤ \right\} \\ \left\{ \frac{m^ 2-2} n : n,m∈ℤ,n≠ 0 \right\} \quad ,\quad \left\{ \frac{m+1}{m^ 2} : m∈ℤ,m≠ 0 \right\} \end{eqnarray*}

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