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Today's calculation of Integral 382

Source: 1992 Tokyo Medical & Dental university entrance exam

October 20, 2008
calculusintegrationlimitcalculus computations

Problem Statement

(1) For a>0, b≥0 a>0,\ b\geq 0, Compare \int_b^{b\plus{}1} \frac{dx}{\sqrt{x\plus{}a}},\ \frac{1}{\sqrt{a\plus{}b}},\ \frac{1}{\sqrt{a\plus{}b\plus{}1}}. (2) Find \lim_{n\to\infty} \sum_{k\equal{}1}^n \frac{1}{\sqrt{n^2\plus{}k}}.
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