Question Number 6238 by sanusihammed last updated on 19/Jun/16 Answered by Yozzii last updated on 20/Jun/16 $${Let}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+{n}^{−\mathrm{1}} \right)^{−{n}^{\mathrm{2}} } ={l}. \\ $$$${Let}\:{u}={n}^{−\mathrm{1}} \Rightarrow{l}=\underset{{u}\rightarrow\mathrm{0}^{+} }…
Question Number 137282 by mathlove last updated on 31/Mar/21 Answered by EDWIN88 last updated on 31/Mar/21 $$\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{fofofof}\right)\left(\mathrm{x}\right)=\mathrm{f}\:'\left(\mathrm{x}\right)\mathrm{f}\:'\left(\mathrm{f}\left(\mathrm{x}\right)\right)\mathrm{f}\:'\left(\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\right)\:\mathrm{f}\:'\left(\mathrm{f}\left(\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\right)\right) \\ $$ Answered by floor(10²Eta[1]) last updated on…
Question Number 137280 by mathlove last updated on 31/Mar/21 Answered by EDWIN88 last updated on 31/Mar/21 $$\Leftrightarrow\:\mathrm{y}\:=\:\mathrm{x}^{\left(\frac{\pi}{\mathrm{ln}\:\mathrm{x}}\right)} =\:\mathrm{x}^{\pi\mathrm{log}\:_{\mathrm{x}} \left(\mathrm{e}\right)} \\ $$$$\Leftrightarrow\:\mathrm{y}=\:\mathrm{x}^{\mathrm{log}\:_{\mathrm{x}} \left(\mathrm{e}^{\pi} \right)} \:;\:\mathrm{y}\:=\:\mathrm{e}^{\pi} \:\Rightarrow\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{0}.…
Question Number 6186 by sanusihammed last updated on 17/Jun/16 $${If}\:{f}\left({x}\right)\:=\:\mathrm{2}{x}\:\:{and}\:\:{ff}\left({x}\right)\:=\:{x}\:+\:\mathrm{1}\: \\ $$$${then}\:{x}\:=\:? \\ $$ Commented by Rasheed Soomro last updated on 17/Jun/16 $${If}\:{f}\left({x}\right)\:=\:\mathrm{2}{x}\:\:{and}\:\:{ff}\left({x}\right)\:=\:{x}\:+\:\mathrm{1}\: \\ $$$${then}\:{x}\:=\:?…
Question Number 6133 by sanusihammed last updated on 15/Jun/16 $${Find}\:{all}\:{positive}\:{integers}\:{n}\:{for}\:{which}\:{there}\:{exist}\:{non}\:{negative} \\ $$$${integer}\:\:{a}_{\mathrm{1}\:} ,\:{a}_{\mathrm{2}} \:,\:{a}_{\mathrm{3}} \:,\:\:…..\:,\:{a}_{{n}\:} .\:\:\:{Such}\:{that}\:. \\ $$$$\frac{\mathrm{1}}{\mathrm{2}^{{a}_{\mathrm{1}} } }+\frac{\mathrm{1}}{\mathrm{2}^{{a}_{\mathrm{2}} } }+…..+\frac{\mathrm{1}}{\mathrm{2}^{{a}_{{n}} } }\:\:=\:\:\frac{\mathrm{1}}{\mathrm{3}^{{a}_{\mathrm{1}} }…
Question Number 71664 by mathmax by abdo last updated on 18/Oct/19 $${find}\:{nature}\:{of}\:{the}\:{sequence}\:{U}_{{n}} =\frac{\mathrm{1}}{{n}}\left(\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}}\right)^{\mathrm{2}} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 5988 by sanusihammed last updated on 08/Jun/16 $${If}\:\:\:\:{ur}\:=\:{log}\:{r} \\ $$$${show}\:{that}\:\:\:\sum_{{r}\:=\:\mathrm{1}} ^{\mathrm{10}} \:{ur}\:=\:{log}\mathrm{3628800} \\ $$$$ \\ $$$${please}\:{help}. \\ $$ Answered by Yozzii last updated…
Question Number 5892 by sanusihammed last updated on 04/Jun/16 $${A}\:\:=\:\:\left[−\mathrm{3}\:\:\:\:\:\mathrm{0}\:\right] \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\left[\:\:\:\:\mathrm{1}\:\:\:\:\:\mathrm{5}\:\right] \\ $$$${And}\:{f}\left({x}\right)\:=\:\mathrm{5}{x}^{\mathrm{2}} \:−\:\mathrm{7}{x}\:+\:\mathrm{8} \\ $$$$ \\ $$$${Find}\:{f}\left({A}\right) \\ $$$$ \\ $$$${please}\:{help}. \\ $$…
Question Number 136861 by bramlexs22 last updated on 27/Mar/21 $$\mathrm{Given}\:\mathrm{f}\left(\sqrt{\mathrm{x}+\mathrm{9}}\:\right)=\:\mathrm{5x}\:\mathrm{and}\:\mathrm{f}\left(\mathrm{a}\right)=\mathrm{4a}^{\mathrm{2}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}. \\ $$$$ \\ $$ Answered by EDWIN88 last updated on 27/Mar/21 $$\:\mathrm{we}\:\mathrm{have}\:\begin{cases}{\mathrm{a}=\sqrt{\mathrm{x}+\mathrm{9}}\:,\:\mathrm{x}=\mathrm{a}^{\mathrm{2}} −\mathrm{9}}\\{\mathrm{4a}^{\mathrm{2}}…
Question Number 71301 by turbo msup by abdo last updated on 13/Oct/19 $${let}\:{f}\left({x}\right)=\int_{\mathrm{1}+{x}} ^{\mathrm{1}+{x}^{\mathrm{2}} } \:\frac{{arctan}\left({xt}+\mathrm{2}\right)}{{x}+{t}}{dt} \\ $$$${calculate}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{x}\rightarrow\mathrm{0}} {f}\left({x}\right) \\ $$ Terms…