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📅 May 10, 2026 👤 scraface

May 10, 2026

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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....
$\sec x + \csc x \approx 11.025$, 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 g...

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