Category: Limits

Question Number 80614 by M±th+et£s last updated on 04/Feb/20 Commented by mathmax by abdo last updated on 04/Feb/20 $$A_n=\frac{1}{n}\sum _{k=1}^{n}ln(a+\frac{k}{n})\Rightarrow A_{n}isaRiemansum$$$${and}\:{lim}_{{n}\rightarrow+\infty}…

Question Number 80585 by ahmadshahhimat775@gmail.com last updated on 04/Feb/20 Commented by kaivan.ahmadi last updated on 04/Feb/20 $$2.$$$${lim}_{x\to \frac{\pi }{6}}\frac{2sin2x+cosx}{2sin2x-3cosx}=\frac{\sqrt{3}+\frac{\sqrt{3}}{2}}{\sqrt{3}-\frac{3\sqrt{3}}{2}}=\frac{\frac{3\sqrt{3}}{2}}{\frac{-\sqrt{3}}{2}}=-3$$ Commented by kaivan.ahmadi…

Question Number 146043 by liberty last updated on 10/Jul/21 Answered by iloveisrael last updated on 10/Jul/21 $$\left(2\right)\underset{x\to 0}{\lim }\frac{{\mathrm{e}}^{\sin \mathrm{x}}-1-\sin \mathrm{x}}{{\left({\tan }^{-1}\left(\sin \mathrm{x}\right)\right)}^2}$$$$\:\mathrm{let}\:\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{sin}\:\mathrm{x}\right)\:=\:\mathrm{u}\:\rightarrow\mathrm{sin}\:\mathrm{x}=\mathrm{tan}\:\mathrm{u}\: \…

Question Number 80442 by Power last updated on 03/Feb/20 Commented by john santu last updated on 03/Feb/20 $$f{}^{\prime }\left(a\right)hahaha$$ Commented by Power last updated…

Question Number 145951 by ArielVyny last updated on 09/Jul/21 $$\sum _{n⩾1}\frac{{(-1)}^n}{n}=??$$ Answered by Olaf_Thorendsen last updated on 09/Jul/21 $$\frac{\mathrm{1}}{\mathrm{1}+{x}}\:=\:\mathrm{1}−{x}+{x}^{\mathrm{2}} −{x}^{\mathrm{3}} +…\:=\:\underset{{n}=\mathrm{0}} {\overset{\infty}…