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