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Home » \min (\sec x + \csc x)^2 = 8 - Silent Sales Machine

\min (\sec x + \csc x)^2 = 8 - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 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 \( x = 2 \).

📌 Final simplified value and clarification:

📌 The value of \( N(3) \) is \( oxed{19} \), but \( N(x) \) has a removable discontinuity at \( x = 2 \).

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