Sunday, 13 October 2013

distinct ordered pairs

How many distinct ordered pairs (a, b) of non-negative integers satisfy 2 a + 5 b = 100?
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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, ...