Thursday, 15 July 2021

Find the number of permutations \(x_1, x_2, x_3, x_4, x_5\) of numbers \(1, 2, 3, 4, 5\) such that the sum of five products $$x_1x_2x_3 + x_2x_3x_4 + x_3x_4x_5 + x_4x_5x_1 + x_5x_1x_2$$is divisible by \(3.\)
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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, ...