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Am I right in saying that the sequence of functions $f_n(x)=\displaystyle\frac{xn^\alpha}{e^{nx}\times\ln(n)}$ converges pointwise to 0 $\forall{x}\in\mathbb{R}$?

Thanks for any help

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    You are right for $x \ge 0$.2011-10-27

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No, take $x=-1$ then you get $\displaystyle \frac{-e^n n^{\alpha}}{\log(n)}\to-\infty$

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    Then what can we say abou the convergence for x<0? That it diverges to $-\infty$?2016-02-05