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Today's calculation of Integral 357

Source: 1982 Miyagi University of Education entrance exam

July 2, 2008
calculusintegrationgeometrylimitcalculus computations

Problem Statement

For 0<a<1 0<a<1, let S(a) S(a) is the area of the figure bounded by three curves y\equal{}e^x,\ y\equal{}e^{\frac{1\plus{}a}{1\minus{}a}x} and y\equal{}e^{2\minus{}x}. Find lim⁡a→0S(a)a \lim_{a\rightarrow 0} \frac{S(a)}{a}.
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