Category: Relation and Functions

Question Number 6238 by sanusihammed last updated on 19/Jun/16 Answered by Yozzii last updated on 20/Jun/16 $$Let\underset{n\to \mathrm{\infty }}{\lim }{(1+n^{-1})}^{-n^2}=l.$$$${Let}\:{u}={n}^{−\mathrm{1}} \Rightarrow{l}=\underset{{u}\rightarrow\mathrm{0}^{+} }…

Question Number 137280 by mathlove last updated on 31/Mar/21 Answered by EDWIN88 last updated on 31/Mar/21 $$\iff \mathrm{y}={\mathrm{x}}^{\left(\frac{\pi }{\ln \mathrm{x}}\right)}={\mathrm{x}}^{\pi \log {}_{\mathrm{x}}\left(\mathrm{e}\right)}$$$$\Leftrightarrow\:\mathrm{y}=\:\mathrm{x}^{\mathrm{log}\:_{\mathrm{x}} \left(\mathrm{e}^{\pi} \right)} \:;\:\mathrm{y}\:=\:\mathrm{e}^{\pi} \:\Rightarrow\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{0}.…

Question Number 6133 by sanusihammed last updated on 15/Jun/16 $$Findallpositiveintegersnforwhichthereexistnonnegative$$$$integer{a}_1,a_2,a_3,\dots ..,a_n.Suchthat.$$$$\frac{\mathrm{1}}{\mathrm{2}^{{a}_{\mathrm{1}} } }+\frac{\mathrm{1}}{\mathrm{2}^{{a}_{\mathrm{2}} } }+…..+\frac{\mathrm{1}}{\mathrm{2}^{{a}_{{n}} } }\:\:=\:\:\frac{\mathrm{1}}{\mathrm{3}^{{a}_{\mathrm{1}} }…

Question Number 5988 by sanusihammed last updated on 08/Jun/16 $$Ifur=logr$$$$showthat\sum _{r=1}^{10}ur=log3628800$$$$$$$$pleasehelp.$$ Answered by Yozzii last updated…

Question Number 136861 by bramlexs22 last updated on 27/Mar/21 $$\mathrm{Given}\mathrm{f}\left(\sqrt{\mathrm{x}+9}\right)=5\mathrm{x}\mathrm{and}\mathrm{f}\left(\mathrm{a}\right)={4\mathrm{a}}^2$$$$\mathrm{find}\mathrm{the}\mathrm{possible}\mathrm{value}\mathrm{of}\mathrm{a}.$$$$$$ Answered by EDWIN88 last updated on 27/Mar/21 $$\:\mathrm{we}\:\mathrm{have}\:\begin{cases}{\mathrm{a}=\sqrt{\mathrm{x}+\mathrm{9}}\:,\:\mathrm{x}=\mathrm{a}^{\mathrm{2}} −\mathrm{9}}\{\mathrm{4a}^{\mathrm{2}}…