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\item[(i)]$x\geqq0$のとき$\displaystyle\sqrt{x}\leqq\frac{1}{2}(x+1)$を示せ．
\item[(ii)]$\displaystyle\int_0^k\sqrt{x}{ \left( 1-\frac{x}{k} \right) }^kdx<1$を示せ($k$は自然数)．
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