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Home » So unless theres a missing number, but there isnt. - Treasure Valley Movers

So unless theres a missing number, but there isnt. - Treasure Valley Movers

📅 April 16, 2026 👤 scraface

Apr 16, 2026

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Define the function:
f(u) = \frac{1}{u^2} + \frac{2}{u} + 1 + 2u, \quad 0 < u \leq \frac{1}...
We now find the maximum of $f(u)$ on this interval. Note that as $u \t...
But wait: as $u \to 0^+$, $\frac{1}{u^2} \to \infty$, so $f(u) \to \in...
Let’s test at $x = \frac{\pi}{4}$: $\sin x = \cos x = \frac{\sqrt{2}}{...
So $u = \frac{1}{2}$ at $x = \frac{\pi}{4}$, and $f\left(\frac{1}{2}\r...
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?

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