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Define \(f: \mathbb{R} \rightarrow \mathbb{R}\) by \[f(x)= \begin{cases}(1-\cos x) \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, ...
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Find all polynomial \(P(x)\) with degree \(\leq n\) and non negative coefficients such that \[P(x)P(\frac{1}{x})\leq P(1)^2\]for all positiv...
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If the maximum and minimum values of \(\sin ^{6} x+\cos ^{6} x,\) as \(x\) takes all real values, are \(a\) and \(b\), respectively, then \(...
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Find the number of ways \(66\) identical coins can be separated into three nonempty piles so that there are fewer coins in the first pile th...
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