Friday, 11 October 2013

r = s

Let R and S be two cubes with sides of length r and s respectively, where r and s are natural numbers.
Show that the difference of their volumes equals to the difference of their surface areas, 
if and only if r = s. 

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Define f:RR by \[f(x)= \begin{cases}(1-\cos x) \sin \left(\frac{1}{x}\right), & x \neq 0 \ 0, ...