Category: Limits

Question Number 181901 by SATYA121993 last updated on 01/Dec/22 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 116317 by bemath last updated on 03/Oct/20 $$\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\left(\frac{\sqrt{\mathrm{n}+1}+\sqrt{\mathrm{n}+2}+\sqrt{\mathrm{n}+3}+\dots +\sqrt{2\mathrm{n}-1}}{{\mathrm{n}}^{\frac{3}{2}}}\right)=$$ Answered by Bird last updated on 03/Oct/20 $${U}_{{n}} \:=\frac{\mathrm{1}}{{n}^{\frac{\mathrm{3}}{\mathrm{2}}} }\sum_{{k}=\mathrm{1}} ^{{n}−\mathrm{1}}…

Question Number 116167 by Ar Brandon last updated on 01/Oct/20 $$\mathrm{Show}\mathrm{that}\mathrm{\forall }n⩾2\mathrm{the}\mathrm{equation}{x}^n=x+n$$$$\mathrm{admits}\mathrm{a}\mathrm{unique}\mathrm{solution}{\mathrm{u}}_{\mathrm{n}}\in (1,2]$$ Answered by 1549442205PVT last updated on 01/Oct/20 $$\mathrm{Put}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{n}}…

Question Number 116136 by bemath last updated on 01/Oct/20 $${\mathrm{y}}^{\prime }=\frac{\mathrm{y}}{\mathrm{x}}+\frac{{2\mathrm{x}}^3\cos \left({\mathrm{x}}^2\right)}{\mathrm{y}}$$$$\mathrm{where}\mathrm{y}\left(\sqrt{\pi }\right)=0$$ Answered by mindispower last updated on 01/Oct/20 $$\frac{{y}}{{x}}={z} \…

Question Number 181602 by ali009 last updated on 27/Nov/22 $$if$$$$\underset{x\to 1}{lim}\frac{\sqrt{ax+b}-4}{(x-1)}=5finda,b$$ Answered by aleks041103 last updated on 27/Nov/22 $$asthedenominatorgoesto0,tohave$$$${a}\:{finite}\:{limit},\:{we}\:{need}\:\sqrt{{ax}+{b}}−\mathrm{4}\rightarrow\mathrm{0}…