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 Mar15 awarded Notable Question Dec8 awarded Caucus Nov8 accepted Proof of identity involving binomial coefficient Nov8 asked Proof of identity involving binomial coefficient Oct25 accepted Nested square brackets in tensor indices Oct18 comment Nested square brackets in tensor indices Is the second 1/2 in the original answer correct? Oct18 asked Nested square brackets in tensor indices Aug5 awarded Yearling Jul2 awarded Curious Apr16 accepted Average IQ of Mensa Apr12 awarded Nice Question Apr11 awarded Popular Question Apr11 asked Average IQ of Mensa Feb27 awarded Popular Question Feb13 comment Limit of $\sqrt[x]{\frac{\tan x}{x}}$ as $x \to 0$ Using your method, what is $\left(\frac{\tan x}{x}\right)^\frac{1}{x^2}$ for $x \to 0$? Feb13 comment Limit of $\sqrt[x]{\frac{\tan x}{x}}$ as $x \to 0$ The power in my first example is $1/x$, in my second it's $1/x^2$. None of theam head to zero for $x \to 0$. Feb13 comment Limit of $\sqrt[x]{\frac{\tan x}{x}}$ as $x \to 0$ @DavidMitra: Using your argument, $(\tan x / x)^{1/x^2}$ should go to $1$ for $x \to 0$ as well. But it's $\sqrt[3]{e}$. See wolframalpha.com/input/… Feb13 accepted Limit of $\sqrt[x]{\frac{\tan x}{x}}$ as $x \to 0$ Feb13 revised Limit of $\sqrt[x]{\frac{\tan x}{x}}$ as $x \to 0$ Replaced $\cos$ by $\sin$, because wrong. Does not change the results. Feb13 asked Limit of $\sqrt[x]{\frac{\tan x}{x}}$ as $x \to 0$