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Home » Nailed Every Exam? Try These Pro Bonus Questions Before Your Test! - Databee Business Systems

Nailed Every Exam? Try These Pro Bonus Questions Before Your Test! - Databee Business Systems

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 In an ecological study, the interaction between two species is modeled by the function \( h(x, y) = \frac{xy}{x^2 + y^2 + 1} \). Find the value of \( h(x, y) \) when \( x = y \) and \( x \to 1 \).

📌 Given \( h(x, y) = \frac{xy}{x^2 + y^2 + 1} \), evaluate at \( x = y \):

📌 \[ h(x, x) = \frac{x \cdot x}{x^2 + x^2 + 1} = \frac{x^2}{2x^2 + 1} \]

📌 Now assess the limit as \( x \to 1 \):

📌 \[ \lim_{x \to 1} h(x, x) = \frac{1^2}{2(1)^2 + 1} = \frac{1}{2 + 1} = \frac{1}{3} \]

📌 Thus, the limiting value is \(\boxed{\frac{1}{3}}\).

📌 A computational linguist uses a cubic model \( p(u) = u^3 - 3u^2 + 2u \) to analyze syntactic complexity. Determine the number of distinct real roots of \( p(u) = 0 \).

📌 We solve \( p(u) = u^3 - 3u^2 + 2u = 0 \).

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