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(Solved): Consider the following sequences of functions and their integrals. Check whether the pointwise limit ...



Consider the following sequences of functions and their integrals. Check whether the pointwise limit function is integrable and whether you can change limit operation and integration:

(i) fn(x) = nx exp (−nx) on [0, 10]

(ii) f (x)= xn /(1+x)2 on [0,1]


(iii) fn(x) = n on [1/k, 2/k] and fn(x) = 0 elsewhere on [0, 2].



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