Let f(x)=limn→∞⎛⎜⎜⎝nn(x+n)(x+n2)⋯(x+nn)n!(x2+n2)(x2+n24 – InterviewSolution

1.	Let f(x)=limn→∞⎛⎜⎜⎝nn(x+n)(x+n2)⋯(x+nn)n!(x2+n2)(x2+n24)⋯(x2+n2n2)⎞⎟⎟⎠xn, for all x>0. Then
Answer» $Let f (x) = lim n \to \infty {⎛ ⎜⎜ ⎝ \frac{n^{n} (x + n) (x + \frac{n}{2}) \dots (x + \frac{n}{n})}{n! (x^{2} + n^{2}) (x^{2} + \frac{n^{2}}{4}) \dots (x^{2} + \frac{n^{2}}{n^{2}})} ⎞ ⎟⎟ ⎠}^{\frac{x}{n}},$ for all $x > 0.$ Then

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