a) Suppose that E is a Jordan region in Rn and that fk E R are integrable on E for k N If fk f uniformly on E as k , prove that f is integrable on E and b) Prove that exists, and find its value for any Jordan region E in R2 lim f(x) dx f(x) dx lim cos(x k)e dA

Question: a) Suppose that E is a Jordan region in Rn and that fk: E R are integrable on E for k N. If fk f

a) Suppose that E is a Jordan region in Rn and that fk: E †’ R are integrable on E for k ˆˆ N. If fk †’ f uniformly on E as k †’ ˆž, prove that f is integrable on E and

b) Prove that

exists, and find its value for any Jordan region E in R2.

lim | f(x) dx = | f(x) dx. lim cos(x/k)e dA

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a Since Uf G Lf G Uf f N G Lf f N G Uf N G Lf N G I1 I2 and f N is integrable we can show that f is ... View full answer

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