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