Question Number 195083 by sciencestudentW last updated on 23/Jul/23 $${x}=\sqrt{\mathrm{5}}−\mathrm{2}\:\:\:\:\: \\ $$$${x}+\frac{\mathrm{1}}{{x}}=? \\ $$ Answered by Rasheed.Sindhi last updated on 23/Jul/23 $${x}=\sqrt{\mathrm{5}}−\mathrm{2}\:\:,\:\:{x}+\frac{\mathrm{1}}{{x}}=? \\ $$$$\frac{\mathrm{1}}{{x}}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}−\mathrm{2}}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}−\mathrm{2}}\centerdot\frac{\sqrt{\mathrm{5}}\:+\mathrm{2}}{\:\sqrt{\mathrm{5}}\:+\mathrm{2}} \\…
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Question Number 195079 by sonukgindia last updated on 23/Jul/23 Answered by witcher3 last updated on 24/Jul/23 $$\mathrm{we}\:\mathrm{applie}\:\mathrm{S}_{\mathrm{n}} \:\mathrm{to}\:\mathrm{this}\:\mathrm{sum}\:\mathrm{witch}\:\mathrm{symetric}\:\mathrm{Groupe}\:\mathrm{of} \\ $$$$\mathrm{n}\:\mathrm{element}\:\mathrm{we}\:\mathrm{not}\:\mathrm{this}\:\mathrm{elements}\:\sigma \\ $$$$\mathrm{cardS}_{\mathrm{n}} =\mathrm{n}!;\left\{\mathrm{1}…..\mathrm{n}\right\}\overset{\sigma} {\rightarrow}\left\{\mathrm{1},….,\mathrm{n}\right\} \\…
Question Number 195075 by tri26112004 last updated on 23/Jul/23 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{sin}^{\mathrm{2}} {x}−{cos}^{\mathrm{3}} {x}}{{x}} \\ $$ Answered by MM42 last updated on 23/Jul/23 $$\exists\:{m}>\mathrm{0}\:;\:\forall\:{x}\in\mathbb{R}\:\Rightarrow\:\mid{sin}^{\mathrm{2}} {x}−{cos}^{\mathrm{3}} {x}\mid\leqslant{m}…
Question Number 195038 by sciencestudentW last updated on 22/Jul/23 $${prove}\:{that}\:{x}+{y}=\frac{\mathrm{1}}{{x}−{y}} \\ $$ Commented by Frix last updated on 22/Jul/23 $$\mathrm{It}'\mathrm{s}\:\mathrm{wrong},\:\mathrm{i}.\mathrm{e}.\:{x}=\mathrm{2}\wedge{y}=\mathrm{3}\:\Rightarrow\: \\ $$$${x}+{y}=\mathrm{5}\:\mathrm{but}\:\frac{\mathrm{1}}{{x}−{y}}=−\mathrm{1} \\ $$$$ \\…
Question Number 195033 by mathlove last updated on 22/Jul/23 $${any}\:{point}\:{is}\:{the}\:{function}\:{is} \\ $$$${not}\:{continous} \\ $$$${f}\left({x}\right)=\left(\mathrm{4}{x}+\mathrm{8}\right)^{\frac{{ln}\mathrm{45}}{\mathrm{8}}} \\ $$$$\left.{a}\left.\right)\:−\mathrm{8}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{b}\right)\:−\mathrm{2} \\ $$$$\left.{c}\left.\right)\:{no}\:{one}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{d}\right)\:\mathrm{5} \\ $$ Answered by alephzero last updated…
Question Number 195035 by mathlove last updated on 22/Jul/23 $$\sqrt{{i}}=? \\ $$ Answered by alephzero last updated on 22/Jul/23 $$\sqrt{{i}}\:=\:? \\ $$$$\left(\sqrt{{i}}\right)^{\mathrm{2}} \:=\:{i} \\ $$$${e}^{{i}\pi}…
Question Number 195003 by mathlove last updated on 22/Jul/23 $${y}={lnx}^{{x}^{{x}} } \:\:\:\:\:\:\:\:\:{y}^{'} =? \\ $$ Answered by shunmisaki007 last updated on 22/Jul/23 $${y}=\mathrm{ln}\left({x}^{{x}^{{x}} } \right)={x}^{{x}}…
Question Number 195002 by mathlove last updated on 22/Jul/23 $${x}^{\sqrt{{x}}} =\left(\sqrt{{x}}\right)^{{x}} \:\:\:\:\:{x}=? \\ $$ Answered by dimentri last updated on 22/Jul/23 $$\:\:\:\left({x}\right)^{\sqrt{{x}}} \:=\:\left({x}\right)^{\frac{\mathrm{1}}{\mathrm{2}}{x}} \\ $$$$\:\:\left(\mathrm{1}\right)\:\sqrt{{x}}\:=\:\frac{\mathrm{1}}{\mathrm{2}}{x}\Rightarrow{x}−\mathrm{2}\sqrt{{x}}\:=\mathrm{0}…
Question Number 195029 by cortano12 last updated on 22/Jul/23 $$\:\:\:\:\underbrace{ } \\ $$ Answered by MM42 last updated on 22/Jul/23 $${lim}_{{x}\rightarrow\mathrm{0}^{+} } \:\frac{\sqrt{\mathrm{1}+{x}}−\mathrm{1}}{\:\sqrt{\mathrm{3}}{ln}\left(\mathrm{1}+{x}\right)}\:=\overset{{hop}} {\rightarrow}\: \\…