Category: Limits

Question Number 173098 by mathlove last updated on 06/Jul/22 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 107536 by bemath last updated on 11/Aug/20 $$\mathrm{♠}\mathcal{B}e\mathcal{M}ath★$$$$Without{L}^{\prime }Hopitalandseries$$$$find\underset{x\to 0}{\lim }\frac{\tan x-x}{x^3}$$ Commented by bobhans last updated on 12/Aug/20…

Question Number 107516 by bemath last updated on 11/Aug/20 $$⊚\mathcal{B}e\mathcal{M}ath⊚$$$$\underset{t\to 0}{\lim }\frac{1-\sqrt{\cos 2t}}{\sin (\frac{\pi }{2}-t)-\cos 2t}?$$ Answered by bemath last updated on 11/Aug/20 $$\underset{{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{2}{t}}{\mathrm{cos}\:{t}−\mathrm{cos}\:\mathrm{2}{t}}\:×\:\underset{{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{1}+\sqrt{\mathrm{cos}\:\mathrm{2}{t}}}…

Question Number 107500 by Ar Brandon last updated on 11/Aug/20 $$\mathrm{Given}\mathrm{a}\in \mathbb{R}-\{\pm 1\}$$$$1.\mathrm{Show}\mathrm{that}\mathrm{\forall }\mathrm{x}\in \mathbb{R}1-2\mathrm{acos}\left(\mathrm{x}\right)+{\mathrm{a}}^2>0$$$$2.\mathrm{Show}\mathrm{that};$$$$\:\:\:\:\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\prod}}\left(\mathrm{1}−\mathrm{2acos}\left(\frac{\mathrm{2k}\pi}{\mathrm{n}}\right)+\mathrm{a}^{\mathrm{2}} \right)=\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\prod}}\left(\mathrm{a}−\mathrm{e}^{\mathrm{2ik}\pi/\mathrm{n}} \right)\left(\mathrm{a}−\mathrm{e}^{−\mathrm{2ik}\pi/\mathrm{n}} \right)…

Question Number 107414 by bemath last updated on 10/Aug/20 $$⊚\mathcal{B}e\mathbb{M}ath⊚$$$$\underset{x\to 0}{\lim }\frac{2-3\cos {}^{6}x\cos {}^{4}2x\cos {}^{2}4x+\cos x}{36x^2}$$$$$$ Answered by ajfour last…