A = 20 \times 20 = 400

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• l = -\frac{b}{2a} = -\frac{40}{2(-1)} = 20
• Thus, \( w = 40 - 20 = 20 \).
• Calculate the maximum area:
• The largest possible area is \(\boxed{400}\) square meters.
• A quantum computing cryptography expert is analyzing a security function \( M(v) = v - \frac{v^5}{5} \) for noise reduction. If \( m_n \) is defined by \( m_n = M\left(\frac{1}{n}\right) \), find the limit of \( m_n \) as \( n \to \infty \).
• We evaluate the limit of \( m_n = M\left(\frac{1}{n}\right) = \frac{1}{n} - \frac{\left(\frac{1}{n}\right)^5}{5} \) as \( n \to \infty \).

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