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Home » The time taken to travel from A to B is \(\fracd60\) hours. - inBeat

The time taken to travel from A to B is \(\fracd60\) hours. - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 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}

📌 and the function is not defined at \( x = 2 \).

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