Category: Limits

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}…

Question Number 116037 by Rio Michael last updated on 30/Sep/20 $$\underset{x\to 0}{\lim }\frac{{27}^x-1}{9^x-1}=??$$ Answered by bemath last updated on 30/Sep/20 $${let}\:\mathrm{3}^{{x}} =\:{t}\:;\:{t}\rightarrow\mathrm{1}…

Question Number 116029 by bemath last updated on 30/Sep/20 $$\underset{x\to \frac{\pi }{2}}{\lim }\frac{\cos x}{{(1-\sin x)}^{\frac{2}{3}}}=?$$ Answered by bobhans last updated on 30/Sep/20 $$setx=\frac{\pi }{2}+z$$$$\underset{{z}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{−\mathrm{sin}\:{z}}{\left(\mathrm{1}−\mathrm{cos}\:{z}\right)^{\frac{\mathrm{2}}{\mathrm{3}}}…