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Home » A_{\texthexagon} = 6 \cdot \frac{\sqrt3}4 s^2 = 6 \cdot 4\sqrt3 = 24\sqrt3 \text cm^2 - Get link 4share

A_{\texthexagon} = 6 \cdot \frac{\sqrt3}4 s^2 = 6 \cdot 4\sqrt3 = 24\sqrt3 \text cm^2 - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Let’s test at $x = \frac{\pi}{4}$: $\sin x = \cos x = \frac{\sqrt{2}}{2}$, so $u = \frac{1}{2} \cdot \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2} = \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{2}$

📌 So $u = \frac{1}{2}$ at $x = \frac{\pi}{4}$, and $f\left(\frac{1}{2}\right) = \frac{1}{(1/2)^2} + \frac{2}{1/2} + 1 + 2\cdot\frac{1}{2} = 4 + 4 + 1 + 1 = 10$

📌 Now check the behavior as $u \to 0^+$:

📌 \frac{1}{u^2} \to \infty, \quad \frac{2}{u} \to \infty, \quad 2u \to 0

📌 So $f(u) \to \infty$

📌 But this contradicts intuition — is the expression unbounded?

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

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

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