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Initial population at \(t = 0\): - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Let \(a\) be the distance from the wall. Then \(a^2 + 12^2 = 15^2\).

📌 So, \(a^2 + 144 = 225\) â \(a^2 = 81\) â \(a = 9\).

📌 Evaluate the integral \(\int_0^1 (3x^2 + 2x) \, dx\).

📌 Integrate term by term: \(\int 3x^2 dx = x^3\), \(\int 2x dx = x^2\), so \(\int_0^1 (3x^2 + 2x) dx = [x^3 + x^2]_0^1 = (1 + 1) - (0 + 0) = 2\).

📌 A function \(f(x) = rac{x^2 - 4}{x - 2}\) is defined for \(x

📌 e 2\). Simplify and find \(\lim_{x o 2} f(x)\).

📌 Factor numerator: \(x^2 - 4 = (x - 2)(x + 2)\), so \(f(x) = rac{(x - 2)(x + 2)}{x - 2} = x + 2\) for \(x

📌 Thus, \(\lim_{x o 2} f(x) = 2 + 2 = 4\).

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