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lim-x-0-tan-tan-tan-tan-x-n-sin-sin-sin-sin-x-n-x-2-




Question Number 159906 by qaz last updated on 22/Nov/21
lim_(x→0) ((tan tan tan ...tan x_(n) −sin sin sin ...sin x_(n) )/x^2 )=?
$$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\underset{\mathrm{n}} {\underbrace{\mathrm{tan}\:\mathrm{tan}\:\mathrm{tan}\:…\mathrm{tan}\:\mathrm{x}}}−\underset{\mathrm{n}} {\underbrace{\mathrm{sin}\:\mathrm{sin}\:\mathrm{sin}\:…\mathrm{sin}\:\mathrm{x}}}}{\mathrm{x}^{\mathrm{2}} }=? \\ $$
Answered by kaivan.ahmadi last updated on 24/Nov/21
∼lim((x^3 /2)/x^2 )=lim(x/2)=0
$$\sim{lim}\frac{\frac{{x}^{\mathrm{3}} }{\mathrm{2}}}{{x}^{\mathrm{2}} }={lim}\frac{{x}}{\mathrm{2}}=\mathrm{0} \\ $$

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