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Home » The surface area of the rectangular prism is 148 square centimeters. - Dachbleche24

The surface area of the rectangular prism is 148 square centimeters. - Dachbleche24

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Wait: let’s recompute at small $x$, say $x = 0.1$ radians:

📌 $\sin x \approx 0.0998$, $\cos x \approx 0.995$, so $\sec x \approx 1.005$, $\csc x \approx 10.02$

📌 $\sec x + \csc x \approx 11.025$, square $\approx 121.55$

📌 $\sin x + \cos x \approx 1.0948$, square $\approx 1.20$

📌 Sum $\approx 122.75$, which is much larger than 10.

📌 So indeed, as $x \to 0^+$ or $x \to \frac{\pi}{2}^-$, the expression grows without bound.

📌 But is that correct? Let's analyze:

📌 As $x \to 0^+$, $\sec x \to 1$, $\csc x \to \infty$, so $(\sec x + \csc x)^2 \sim \csc^2 x \sim \frac{1}{x^2}$

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