6. (2 p. + 3p. + 3p.) (a) Suppose that E is a Jordan region in R” and that, for each k € N, the function fk: ER is integ

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6 2 P 3p 3p A Suppose That E Is A Jordan Region In R And That For Each K N The Function Fk Er Is Integ 1 (77.44 KiB) Viewed 38 times

6. (2 p. + 3p. + 3p.) (a) Suppose that E is a Jordan region in R” and that, for each k € N, the function fk: ER is integrable. If fk converges to f: E + R uniformly on E, prove the f is integrable on E and that fxdV f(T)dV. lim fu(7)AV = = S, 7. (b) For E = [0, 1] x [0, 1] x [0, 1] and fk: ER given by : fk(x, y, z) = k373 + 2k²y2 + k + 1)3z 3k3 + 11.xyz show that the sequence (fk), converges uniformly on E and find its limit. (c) Prove that the limit below exists and find its value: lim SUL k3x3 + 2k2y2 + (k + 1)3z dzdxdy. 3k3 + 11xyz k-00 VT V.23