Question Number 214228 by mr W last updated on 02/Dec/24 Commented by mr W last updated on 02/Dec/24 $${find}\:{area}\:{of}\:{the}\:{square} \\ $$ Answered by aleks041103 last…
Question Number 214247 by hardmath last updated on 02/Dec/24 $$\mathrm{If}\:\:\:\mathrm{2a}\:=\:\mathrm{1}\:−\:\mathrm{2}\sqrt{\mathrm{a}} \\ $$$$\mathrm{Find}\:\:\:\frac{\mathrm{2a}^{\mathrm{2}} \:+\:\sqrt{\mathrm{a}}}{\mathrm{2a}}\:=\:? \\ $$ Answered by A5T last updated on 02/Dec/24 $$\mathrm{2}{a}=\mathrm{1}−\mathrm{2}\sqrt{{a}}\Rightarrow\begin{cases}{\sqrt{{a}}=\frac{\mathrm{2}{a}−\mathrm{1}}{−\mathrm{2}}}\\{\left(\mathrm{2}{a}−\mathrm{1}\right)^{\mathrm{2}} =\mathrm{4}{a}\Rightarrow\mathrm{4}{a}^{\mathrm{2}} +\mathrm{1}=\mathrm{8}{a}}\end{cases}…
Question Number 214256 by Einstein2006 last updated on 02/Dec/24 $$\boldsymbol{{lim}}_{\boldsymbol{{x}}\:\rightarrow\:\mathrm{1}} \propto.\boldsymbol{{arctan}}\left(\frac{\mathrm{2}}{\mathrm{1}\:+\boldsymbol{{x}}}\:−\:\mathrm{1}\right) \\ $$$$\bullet\:\boldsymbol{{Calculons}}\:\boldsymbol{{la}}\:\boldsymbol{{limite}}\:\boldsymbol{{a}}\:\boldsymbol{{l}}'\boldsymbol{{intrieur}}: \\ $$$$\frac{\mathrm{2}}{\mathrm{1}\:+\:\boldsymbol{{x}}}\:−\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\: \\ $$$$\boldsymbol{{lim}}_{\boldsymbol{{x}}\:\rightarrow\:\mathrm{1}} {arctan}\left(\frac{\mathrm{2}}{\mathrm{1}\:+\:{x}}\:−\:\mathrm{1}\right)=\:\boldsymbol{{arctan}}\left(\mathrm{0}\right)\:=\:\mathrm{0} \\ $$$$\: \\ $$$$\boldsymbol{{lim}}_{\boldsymbol{{x}}\rightarrow\mathrm{1}} \propto.{arctan}\left(\frac{\mathrm{2}}{\mathrm{1}+\:{x}}\:−\:\mathrm{1}\right)\:=\propto.\mathrm{0}\:…
Question Number 214220 by Ari last updated on 01/Dec/24 Answered by mr W last updated on 01/Dec/24 $${say}\:{a}>{b} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={c}^{\mathrm{2}} \:\:\:…\left({i}\right) \\ $$$${a}−{b}=\mathrm{6}\:\:\:…\left({ii}\right)…
Question Number 214205 by MathematicalUser2357 last updated on 01/Dec/24 $${f}\left({x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\right)={x}−\sqrt{{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$${f}\left(\mathrm{2}\right)+{f}\left(\mathrm{3}\right)+{f}\left(\mathrm{6}\right)=? \\ $$ Answered by golsendro last updated on 01/Dec/24 $$\:\:\:\:\underline{\underbrace{\:}} \underline{…
Question Number 214191 by golsendro last updated on 01/Dec/24 $$\:\:\:\:\:\:\begin{cases}{\mathrm{y}^{\mathrm{3}} =\:\mathrm{x}^{\mathrm{x}+\mathrm{y}} }\\{\mathrm{y}^{\mathrm{x}+\mathrm{y}} \:=\:\mathrm{x}^{\mathrm{6}} \mathrm{y}^{\mathrm{3}} }\end{cases} \\ $$$$\:\:\:\:\cancel{\underline{ }} \\ $$ Answered by TonyCWX08 last updated…
Question Number 214216 by MathematicalUser2357 last updated on 01/Dec/24 $${a}_{{n}} ={a}_{{n}−\mathrm{1}} +\frac{{x}−{a}_{{n}−\mathrm{1}} }{{t}} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}{a}_{{n}} =? \\ $$ Answered by mr W last updated…
Question Number 214199 by mr W last updated on 01/Dec/24 Commented by mr W last updated on 01/Dec/24 $$\left[{see}\:{Q}\mathrm{214176}\right] \\ $$$${find}\:{the}\:{radius}\:{of}\:{the}\:{maximal} \\ $$$${circle}\:{inscribed}\:{between}\:{the}\:{curves} \\ $$$${f}\left({x}\right)\:{and}\:{g}\left({x}\right)\:{as}\:{shown}.…
Question Number 214186 by hardmath last updated on 30/Nov/24 $$\mathrm{If}\:\:\:\mathrm{x}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\:=\:\mathrm{1}\:\:\:\mathrm{find}\:\:\:\mathrm{x}^{\mathrm{61}} \:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{61}} }+\:\mathrm{4}\:\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on 30/Nov/24 $${x}+\frac{\mathrm{1}}{{x}}=\mathrm{1};\:{x}^{\mathrm{61}} +\frac{\mathrm{1}}{{x}^{\mathrm{61}} }+\mathrm{4}=? \\…
Question Number 214181 by golsendro last updated on 30/Nov/24 $$\:\:\:\:\underbrace{\:} \\ $$ Answered by efronzo1 last updated on 30/Nov/24 $$\:\:\:\cancel{\nprec} \\ $$ Terms of Service…