Category: Limits

Question Number 73251 by aliesam last updated on 09/Nov/19 Answered by mind is power last updated on 09/Nov/19 $$\mathrm{E}\left({\mathrm{u}}_{\mathrm{n}}\right)⩽{\mathrm{u}}_{\mathrm{n}}<\mathrm{E}\left({\mathrm{u}}_{\mathrm{n}}\right)+1={\mathrm{U}}_{\mathrm{n}+1}$$$$\Rightarrow\mathrm{U}_{\mathrm{n}} \mathrm{is}\:\mathrm{a}\:\mathrm{creasing}\:\mathrm{squances}…

Question Number 138767 by bramlexs22 last updated on 18/Apr/21 $$\underset{x\to 0}{\lim }\frac{\tan \left(\pi \cos {}^{2}x\right)}{\sin \left(2\pi \sin {}^{2}x\right)}=?$$ Answered by EDWIN88 last updated on 18/Apr/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\left(\pi\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\right)}{\mathrm{sin}\:\left(\mathrm{2}\pi\mathrm{sin}\:^{\mathrm{2}}…

Question Number 73200 by aliesam last updated on 07/Nov/19 $$if$$$$$$$$\underset{x\to 0^{+}}{limf}\left(x\right)=+\mathrm{\infty }$$$$$$$$\underset{x\to 0^{-}}{limf}\left(x\right)=+\mathrm{\infty }$$$$ \…

Question Number 138735 by SanyamJoshi last updated on 17/Apr/21 Answered by Ajaypareek last updated on 17/Apr/21 $$1$$ Answered by bramlexs22 last updated on…

Question Number 73117 by aliesam last updated on 06/Nov/19 Commented by mathmax by abdo last updated on 06/Nov/19 $$wehavecos\left(3x\right)\sim 1-\frac{{\left(3x\right)}^2}{2}(x\to 0)\Rightarrow cos\left(3x\right)-1\sim -\frac{9x^2}{2}\Rightarrow$$$$\mathrm{1}−{cos}\left(\mathrm{3}{x}\right)\sim\frac{\mathrm{9}{x}^{\mathrm{2}} }{\mathrm{2}}\:\Rightarrow\frac{\mathrm{1}−{cos}\left(\mathrm{3}{x}\right)}{{x}^{\mathrm{2}} }\sim\frac{\mathrm{9}}{\mathrm{2}}\:\Rightarrow{lim}_{{x}\rightarrow\mathrm{0}}…