Suppose (x, y) is continuous over a region R in the plane and that the area A(R)
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Suppose ƒ(x, y) is continuous over a region R in the plane and that the area A(R) of the region is defined. If there are constants m and M such that m ≤ ƒ(x, y) ≤ M for all (x, y)ε R, prove that
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mA(R) < ffs f(x, y) dAMA(R). R
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Since x y is continuous over R by the Extreme Value Theorem it must attain a minimum value m an...View the full answer
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Related Book For
Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir
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