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Q51Section II (Mathematics)51 of 190

Two classical oscillating functions — neither is of bounded variation

Let f,g:R→Rf,g:\mathbb{R}\to\mathbb{R} be defined by f(x)=sin⁡1xf(x)=\sin\dfrac1x and g(x)=xsin⁡1xg(x)=x\sin\dfrac1x (suitably defined at 00). Then:

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