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Home » \( d = 400 \) - Roya Kabuki

\( d = 400 \) - Roya Kabuki

📅 May 9, 2026 👤 scraface

May 09, 2026

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📌 A community health researcher studies nutrient concentration in soil, modeled by \( N(x) = rac{x^3 - 8}{x - 2} \). Find \( N(3) \) in simplest form and determine whether the function is defined at \( x = 2 \).

📌 First, simplify \( N(x) = rac{x^3 - 8}{x - 2} \). Recognize the numerator as a difference of cubes:

📌 x^3 - 8 = (x - 2)(x^2 + 2x + 4)

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

📌 Now evaluate \( N(3) \):

📌 N(3) = 3^2 + 2(3) + 4 = 9 + 6 + 4 = 19

📌 The function is undefined at \( x = 2 \) because of division by zero, even though the simplified form gives \( N(2) = 2^2 + 2(2) + 4 = 12 \), which matches the limit. But at \( x = 2 \), the original expression is undefined.

📌 N(3) = oxed{19}

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