Category: Limits

Question Number 99697 by Ar Brandon last updated on 22/Jun/20 $$\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\underset{\mathrm{k}=0}{\sum ^{2\mathrm{n}}}\frac{\mathrm{k}}{\mathrm{k}+{\mathrm{n}}^2}$$ Commented by MWSuSon last updated on 22/Jun/20 just dropping a comment so that I'll get notified when someone solves it. if only the k in the denominator was k^2��…

Question Number 99676 by bemath last updated on 22/Jun/20 $$\underset{x\to 0}{\lim }\frac{\sin \left(\sin \mathrm{x}\right)-\mathrm{x}}{\mathrm{x}(\cos \left(\sin \mathrm{x}\right)-1)}??$$ Answered by bobhans last updated on 23/Jun/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\mathrm{x}−\frac{\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}}{\mathrm{6}}\:−\mathrm{x}}{\mathrm{x}\left(\mathrm{1}−\frac{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}{\mathrm{2}}\:−\mathrm{1}\right)}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{x}−\frac{\mathrm{x}^{\mathrm{3}}…

Question Number 99600 by bemath last updated on 22/Jun/20 Answered by mathmax by abdo last updated on 22/Jun/20 $${\mathrm{y}}^{{}^{″}}+{3\mathrm{y}}^{{}^{\prime }}+2\mathrm{y}=\sin \left({\mathrm{e}}^{\mathrm{x}}\right)$$$$\left(\mathrm{he}\right)\rightarrow\mathrm{y}^{''} \:+\mathrm{3y}^{'}…

Question Number 34007 by rahul 19 last updated on 29/Apr/18 $$\underset{x\to 2}{\lim }\frac{\sqrt{x-2}+\sqrt{x}-\sqrt{2}}{\sqrt{x^2-4}}is?$$ Answered by tanmay.chaudhury50@gmail.com last updated on 29/Apr/18 $$={li}\underset{{x}\rightarrow\mathrm{2}} {{m}}\frac{\sqrt{{x}−\mathrm{2}\:}\:+\left({x}−\mathrm{2}\right)/\left(\sqrt{{x}}\:+\sqrt{\mathrm{2}}\right)}{\:\sqrt{\left({x}+\mathrm{2}\right)\left({x}−\mathrm{2}\right)}\:} \…

Question Number 33942 by manishprajapati076@gmail.com last updated on 28/Apr/18 Commented by manishprajapati076@gmail.com last updated on 28/Apr/18 $$solve1211\mathrm{no}.$$ Answered by MJS last updated on…