Question Number 196066 by sniper237 last updated on 17/Aug/23 $$\begin{pmatrix}{\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:−\mathrm{1}}\\{−\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}}\end{pmatrix}^{−\mathrm{8}} =\:\:? \\ $$ Answered by witcher3 last updated on 17/Aug/23 $$\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:−\mathrm{1}}\\{−\mathrm{1}\:\:\:\:\:\:\mathrm{2}}\end{pmatrix}=\mathrm{A} \\ $$$$\mathrm{A}^{\mathrm{2}} =\begin{pmatrix}{\mathrm{2}\:\:\:\:\:−\mathrm{3}}\\{−\mathrm{3}\:\:\:\:\mathrm{3}}\end{pmatrix}=\mathrm{3A}−\mathrm{I}_{\mathrm{2}} \\…
Question Number 196024 by York12 last updated on 16/Aug/23 $$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\left[{x}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{{n}^{{x}+\mathrm{1}} }\right)\right]=\lambda\:,\:{evalute}\:\lambda \\ $$ Answered by mr W last updated on 16/Aug/23…
Question Number 196026 by Erico last updated on 16/Aug/23 $$\underset{\:\mathrm{0}} {\int}^{\:+\infty} \frac{\left({lnt}\right)^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$ Answered by sniper237 last updated on 16/Aug/23 $$=\:{f}''\left(\mathrm{0}\right)\:\:\:{with}\:\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty}…
Question Number 196037 by cortano12 last updated on 16/Aug/23 $$\:\:\:\int\:\frac{\mathrm{sin}\:\mathrm{2x}}{\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{3}} \mathrm{x}}\:\mathrm{dx}\:=? \\ $$ Answered by Frix last updated on 16/Aug/23 $$\mathrm{Use}\:{t}=\mathrm{sin}\:\left({x}−\frac{\pi}{\mathrm{4}}\right)\:\Rightarrow\:{dx}=\frac{{dt}}{\:\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}\:\mathrm{to}\:\mathrm{get} \\ $$$$\sqrt{\mathrm{2}}\int\frac{\mathrm{2}{t}^{\mathrm{2}}…
Question Number 196021 by universe last updated on 16/Aug/23 Answered by mr W last updated on 17/Aug/23 Commented by mr W last updated on 17/Aug/23…
Question Number 196023 by pticantor last updated on 16/Aug/23 $${find}\:{the}\:{domain}\:{of}\:{definition}\:{of}\:{this} \\ $$$$\left.{function}\:{for}\:{t}\in\right]\mathrm{0};\mathrm{1}\left[\right. \\ $$$$\:\:\:\:\:\boldsymbol{\rho}\left({x}\right)=\int_{{x}} ^{\mathrm{2}{x}} \frac{\mathrm{1}}{{lnt}}{dt} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{ptiCantor} \\ $$ Answered by sniper237 last updated…
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Question Number 195996 by sonukgindia last updated on 15/Aug/23 Answered by Rasheed.Sindhi last updated on 15/Aug/23 $${Let}\:{radius}\:{of}\:{blue}\:{quarter}={r} \\ $$$${and}\:{of}\:{green}={R} \\ $$$${R}={r}+\mathrm{1} \\ $$$${Diagonal}={R}+{r} \\ $$$$\left({R}+{r}\right)^{\mathrm{2}}…
Question Number 195998 by Frix last updated on 15/Aug/23 $$\mathrm{We}\:\mathrm{can}\:\mathrm{transform}\:\mathrm{to}\:\mathrm{get}\:\mathrm{rid}\:\mathrm{of}\:\mathrm{the}\:\sqrt[{\mathrm{3}}]{…} \\ $$$${a}^{\frac{\mathrm{1}}{\mathrm{3}}} +{b}^{\frac{\mathrm{1}}{\mathrm{3}}} ={c}^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$$$\left({a}^{\frac{\mathrm{1}}{\mathrm{3}}} +{b}^{\frac{\mathrm{1}}{\mathrm{3}}} \right)^{\mathrm{3}} ={c} \\ $$$${a}+{b}+\mathrm{3}{a}^{\frac{\mathrm{1}}{\mathrm{3}}} {b}^{\frac{\mathrm{1}}{\mathrm{3}}} \left({a}^{\frac{\mathrm{1}}{\mathrm{3}}} +{b}^{\frac{\mathrm{1}}{\mathrm{3}}} \right)={c}…