Evaluate a limit without Taylor series – math.stackexchange.com

Evaluate a limit without Taylor series – math.stackexchange.com

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Evaluate $$\lim_{x\to 0}\frac{(\tan x)^{2008}-(\arctan x)^{2008}}{x^{2009}}$$ without using Taylor series. I have a solution using $\lim_{x\to 0}\frac{\tan x-\arctan x}{x^2}=0$, but I would really ...

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