Category: Limits

Question Number 197832 by mathlove last updated on 30/Sep/23 $$\underset{x\to \mathrm{\infty }}{\lim }\frac{2+\sqrt{cosx}}{-1+\sqrt{cosx}}=?$$ Answered by MM42 last updated on 30/Sep/23 $$letf\left(x\right)=\frac{2+\sqrt{cosx}}{-1+\sqrt{cosx}}$$$${for}\:\:{a}_{{n}} =\mathrm{2}{n}\pi\Rightarrow{lim}_{{n}\rightarrow\infty} \:{f}\left({a}_{{n}}…

Question Number 197661 by pticantor last updated on 25/Sep/23 $$\mathit{l}\mathit{i}\underset{\mathit{n}\to \mathrm{\infty }}{\mathit{m}}{\int }_0^1\frac{dt}{1+t+\dots .+t^n}=?$$ Commented by JDamian last updated on 25/Sep/23 $$\mathrm{Why}\:\mathrm{do}\:\mathrm{you}\:\mathrm{post}\:\mathrm{again}\:\mathrm{the}\:\mathrm{same}\:\mathrm{topic} \…

Question Number 197610 by mathlove last updated on 24/Sep/23 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 197548 by cortano12 last updated on 21/Sep/23 $$\underset{x\to -\mathrm{\infty }}{\lim }{\left(\frac{4\mathrm{x}-\sqrt{{4\mathrm{x}}^2+5}}{2\mathrm{x}-1}\right)}^{\mathrm{bx}}=?$$ Answered by MM42 last updated on 21/Sep/23 $${lim}_{{x}\rightarrow−\infty} \:\left(\frac{\mathrm{4}{x}−\mid\mathrm{2}{x}\mid}{\mathrm{2}{x}−\mathrm{1}}\right)^{{bx}} ={lim}_{{x}\rightarrow−\infty}…

Question Number 197514 by cortano12 last updated on 20/Sep/23 $$\underset{x\to \mathrm{\infty }}{\lim }\sin \mathrm{x}{\sin }^{-1}\left(\frac{1}{\mathrm{x}}\right)=?$$ Answered by MM42 last updated on 20/Sep/23 $$\frac{\mathrm{1}}{{x}}={t}\Rightarrow{lim}_{{t}\rightarrow\mathrm{0}} \:{sin}\frac{\mathrm{1}}{{t}}×{sin}^{−\mathrm{1}} {t}\:=\mathrm{0} \…