Saturday, 3 October 2015

analysis - limtrightarrowinftyfractnzn|tnzn+cdots+tz+c|?



How to find the limit




lim
where c \in\Bbb C?





is the answer z^n? please help :)




Answer



\lim_{t\to\infty}\frac{t^n z^n}{|t^nz^n + \ldots+tz +c|}=\lim_{t\to\infty}\frac{z^n}{\left|z^n+\frac{z^{n-1}}{t^{n-1}}+\ldots+\frac{c}{t^n}\right|}=\ldots



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