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Today's calculation of Integral 132

Source: Osaka University entrance exam /Economics 1968

August 10, 2006
calculusintegrationgeometryinequalitieslimitlogarithmscalculus computations

Problem Statement

Find the area of the figure such that the points (x, y)(x,\ y) satisfies the inequality lim⁡n→∞(x2n+y2n)1n≥32x2+32y2−1.\lim_{n\to\infty}(x^{2n}+y^{2n})^{\frac{1}{n}}\geq \frac{3}{2}x^{2}+\frac{3}{2}y^{2}-1.
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