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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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In an idle moment, Vedansi Chakraborty picked up two numbers x and y such that 0<x<y<1. She wondered how to combine these simply...
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To each element of the set S = {1, 2,............, 1000} a colour is assigned. Suppose that for any two elements m & n of S, if 15 di...