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Home » Now consider **product modulo small numbers**. Try small cases: - Dachbleche24

Now consider product modulo small numbers. Try small cases: - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 ight) + 9 = 4 \cdot rac{9}{4} - 18 + 9 = 9 - 18 + 9 = 0

📌 Thus, the minimum heat loss is 0 units at \( t = rac{3}{2} \) hours.

📌 oxed{ ext{Minimum heat loss is } 0 ext{ at } t = rac{3}{2} ext{ hours}}

📌 An astrophysicist working on gravitational wave detection models a signal with the equation \( g(t) = rac{t^3 - 8}{t - 2} \). Evaluate \( \lim_{t o 2} g(t) \).

📌 Note that the expression \( rac{t^3 - 8}{t - 2} \) is indeterminate at \( t = 2 \) since both numerator and denominator vanish. Factor the numerator:

📌 t^3 - 8 = (t - 2)(t^2 + 2t + 4)

📌 g(t) = rac{(t - 2)(t^2 + 2t + 4)}{t - 2} = t^2 + 2t + 4 \quad ext{for } t

📌 \lim_{t o 2} g(t) = 2^2 + 2(2) + 4 = 4 + 4 + 4 = 12

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