I need to find $$\lim\limits_{x\mathop\to\infty}\frac{\tan x}{x}$$
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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