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Let f(x) lim( n to infty) [(n^(n)(x+n)...

Let ` f(x) lim_( n to infty) [(n^(n)(x+n)(x+n/2)...(x+n/n))/(n! (x^(2+n^(2)))(x^(2)+n^(2)/4)...(x^(2)+n^(2)/n^(2)))]^(x/n) ` ,for all x = 0 . Then

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