There are natural numbers m & n. Find all the fractions m/n whose denominator is smaller than the
numerator by 16, the fraction itself is smaller than the sum of the trebled
inverse and 2, and the numerator is not greater than 30.
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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, &a...
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Find the number of pairs \((m,n)\) of positive integers with \(1 \le m < n \le 30\) such that there exists a real number \(x\) satisfying...
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