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+1.331 = 4.641 - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Thus, \((\sec x + \csc x)^2\) is unbounded on \(0 < x < \frac{\pi}{2}\), and has no maximum.

📌 But wait — is that correct?

📌 Let \(x \to 0^+\), \(\sec x \to 1\), \(\csc x \to \infty\), so sum \(\to \infty\). Similarly near \(\frac{\pi}{2}^-\). So the expression goes to infinity.

📌 Hence, there is **no maximum value**; it spans \((8, \infty)\).

📌 But let’s verify at \(x = \frac{\pi}{4}\):

📌 \(\sec \frac{\pi}{4} = \sqrt{2}\), \(\csc \frac{\pi}{4} = \sqrt{2}\), sum = \(2\sqrt{2} \approx 2.828\), square ≈ 8, matches \(g(2) = 8\).

📌 But as \(x \to 0^+\), \(f(x) \to \infty\), so no maximum.

📌 Thus, the function has **no maximum value** on the open interval.

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