Question Number 140774 by ajfour last updated on 12/May/21 $${Prove}\:{that} \\ $$$$\:\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}+\frac{\mathrm{5}}{\mathrm{3}\sqrt{\mathrm{6}}}\right)^{\mathrm{1}/\mathrm{3}} +\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}−\frac{\mathrm{5}}{\mathrm{3}\sqrt{\mathrm{6}}}\right)^{\mathrm{1}/\mathrm{3}} =\:\sqrt{\mathrm{2}} \\ $$ Commented by ajfour last updated on 12/May/21 $${All}\:{are}\:{Excellent}\:{solutions}\:: \\…
Question Number 9699 by ridwan balatif last updated on 26/Dec/16 Commented by ridwan balatif last updated on 26/Dec/16 $$\mathrm{how}\:\mathrm{many}\:\mathrm{x}\:\mathrm{can}\:\mathrm{fill}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\left(\mathrm{cos3x}+\mathrm{tan3x}\right)\left(\mathrm{cos3x}−\mathrm{tan3x}\right)=\mathrm{1}\:\mathrm{for} \\ $$$$\mathrm{0}\leqslant\mathrm{x}\leqslant\mathrm{2}\pi,\:\mathrm{x}\neq\frac{\pi}{\mathrm{6}}+\frac{\mathrm{2k}\pi}{\mathrm{3}}\:\mathrm{and}\:\mathrm{k}\:\mathrm{is}\:\left(\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},…\right)\: \\ $$$$\mathrm{is}\:….?…
Question Number 140768 by EDWIN88 last updated on 12/May/21 $$\:\int_{−\infty} ^{\infty} \frac{\mathrm{x}^{\mathrm{2}} +\mathrm{4}}{\mathrm{x}^{\mathrm{4}} +\mathrm{16}}\:\mathrm{dx}\:=? \\ $$ Answered by Ar Brandon last updated on 12/May/21 $$\mathcal{I}=\int_{−\infty}…
Question Number 9698 by rahulrai441992@gmail.com last updated on 26/Dec/16 $${a}^{\mathrm{2}} +{ab}+{b}^{\mathrm{2}} \\ $$ Answered by geovane10math last updated on 26/Dec/16 $${a}^{\mathrm{2}} \:+\:{ab}\:+\:{b}^{\mathrm{2}} \:=\:{a}^{\mathrm{2}} \:+\:\mathrm{2}{ab}\:+\:{b}^{\mathrm{2}} \:−\:{ab}\:=…
Question Number 75230 by aliesam last updated on 08/Dec/19 Commented by mathmax by abdo last updated on 08/Dec/19 $${e}^{\frac{\mathrm{1}}{{x}}} =\mathrm{1}+\frac{\mathrm{1}}{{x}}\:+{o}\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)\:\Rightarrow{x}\:{e}^{\frac{\mathrm{1}}{{x}}} ={x}+\mathrm{1}+{o}\left(\frac{\mathrm{1}}{{x}}\right)\:\:\left({x}\rightarrow+\infty\right) \\ $$$${e}^{\frac{\mathrm{1}}{{x}+\mathrm{1}}} =\mathrm{1}+\frac{\mathrm{1}}{{x}+\mathrm{1}}\:+{o}\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}}…
Question Number 140767 by EDWIN88 last updated on 12/May/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\::\:\mathrm{2cot}\:^{\mathrm{2}} \mathrm{x}\:+\:\mathrm{csc}\:^{\mathrm{2}} \mathrm{x}−\mathrm{2}\:=\:\mathrm{0}\: \\ $$ Answered by Ar Brandon last updated on 12/May/21 $$\mathrm{2cot}^{\mathrm{2}} \mathrm{x}+\mathrm{csc}^{\mathrm{2}} \mathrm{x}−\mathrm{2}=\mathrm{0}…
Question Number 75228 by ~blr237~ last updated on 08/Dec/19 $$\:\mathrm{Let}\:\mathrm{consider}\: \\ $$$$\mathrm{A}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\int_{\mathrm{0}} ^{\mathrm{1}} \left(\Gamma\left(\mathrm{t}\right)\right)^{\mathrm{x}} \mathrm{dt}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\:\mathrm{A}=\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}\left(\Gamma\left(\mathrm{t}\right)\right)\mathrm{dt}\:\: \\ $$$$\mathrm{Deduce}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{A} \\ $$ Commented…
Question Number 9690 by tawakalitu last updated on 24/Dec/16 Commented by ridwan balatif last updated on 25/Dec/16 $$\mathrm{10}\:\mathrm{is}\:\mathrm{radius},\mathrm{right}? \\ $$ Commented by tawakalitu last updated…
Question Number 75224 by ~blr237~ last updated on 08/Dec/19 $$\mathrm{Prove}\:\mathrm{that}\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{xln}\mid\mathrm{x}\mid−\left(\mathrm{x}−\mathrm{m}\right)\mathrm{ln}\mid\mathrm{x}−\mathrm{m}\mid\right)=+\infty \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 75225 by ~blr237~ last updated on 08/Dec/19 $$\mathrm{Prove}\:\mathrm{that}\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{xln}\mid\mathrm{x}\mid−\left(\mathrm{x}−\mathrm{m}\right)\mathrm{ln}\mid\mathrm{x}−\mathrm{m}\mid\right)=+\infty \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com