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Let R an elemental rectangle in R2 and g, f : R → R continuous functions. Show that lim Ef (uij) g (Vij) A ( Rij) = || f(x, y)g(x,y)dA d(P)→0 5 R where P = {Rij :1

Let R an elemental rectangle in R2 and g, f : R → R continuous functions. Show that lim Ef (uij) g (Vij) A ( Rij) = || f(x, y)g(x,y)dA d(P)→0 5 R where P = {Rij :1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let R an elemental rectangle in R2 and g, f : R → R continuous functions. Show that lim Ef(uij) g (vij) A (Rij) = || f(x, y)g(x, y)dA d(P)→0 5 R where P = {R¡ :1<isn, 1<j<m} is a partition by elementary rectangles of R and Uij, Vij any points in Rij.
Transcribed Image Text:Let R an elemental rectangle in R2 and g, f : R → R continuous functions. Show that lim Ef(uij) g (vij) A (Rij) = || f(x, y)g(x, y)dA d(P)→0 5 R where P = {R¡ :1<isn, 1<j<m} is a partition by elementary rectangles of R and Uij, Vij any points in Rij.
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