Monday, 30 July 2018

limits - Evaluating limlimitsxmathoptoinftyfractanxx



I need to find lim

For some reason mathematica just returns my input without evaluating it.



For what it's worth, \dfrac{\tan(10^{100})}{10^{100}}\approx -4\times10^{-101}, so the limit is probably 0. (...)



I'm guessing this has been asked before but I can't find it.


Answer



The limit does not exist: Since the tangent function has poles at every point of the form \left(n + \frac 1 2\right) \pi, the quantity



\frac{\tan x}{x}




is unbounded on every interval of length greater than \pi.


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