Question Number 196596 by MATHEMATICSAM last updated on 27/Aug/23 $$\mathrm{If}\:{f}\left({x}\right)\:=\:\mathrm{ln}\left(\frac{\mathrm{1}\:+\:{x}}{\mathrm{1}\:−\:{x}}\right)\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$${f}\left(\frac{\mathrm{2}{x}}{\mathrm{1}\:+\:{x}^{\mathrm{2}} }\right)\:=\:\mathrm{2}{f}\left({x}\right). \\ $$ Commented by mokys last updated on 27/Aug/23 $${f}\:\left(\frac{\mathrm{2}{x}}{\mathrm{1}+{x}^{\mathrm{2}} }\right)=\:{ln}\left(\frac{\mathrm{1}+\frac{\mathrm{2}{x}}{\mathrm{1}+{x}^{\mathrm{2}} }}{\mathrm{1}−\frac{\mathrm{2}{x}}{\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 196427 by Erico last updated on 24/Aug/23 $$\mathrm{If}\:\:{f}\left({x}\right)=\underset{\:\mathrm{0}} {\int}^{\:{x}} \frac{{dt}}{{t}+{e}^{−{f}\left({t}\right)} },\:\mathrm{determine}\:{f}\left({x}\right) \\ $$ Answered by witcher3 last updated on 25/Aug/23 $$\mathrm{f}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\mathrm{f}'\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\mathrm{x}+\mathrm{e}^{−\mathrm{f}\left(\mathrm{x}\right)}…
Question Number 196249 by mathlove last updated on 20/Aug/23 $${log}_{{a}} {x}=\mathrm{30} \\ $$$${log}_{{b}} {x}=\mathrm{70} \\ $$$${log}_{{ab}} {x}=? \\ $$ Answered by AST last updated on…
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 $$=\:{f}''\left(\mathrm{0}\right)\:\:\:{with}\:\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty}…
Question Number 195895 by Erico last updated on 12/Aug/23 $$\mathrm{Calcul}\:\:\:\:\:\:\:\:\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \mathrm{t}\sqrt{\mathrm{tan}\left(\mathrm{t}\right)}\:\mathrm{dt} \\ $$ Answered by witcher3 last updated on 13/Aug/23 $$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{t}\right).\sqrt{\mathrm{t}}}{\mathrm{1}+\mathrm{t}^{\mathrm{2}}…
Question Number 195753 by Erico last updated on 09/Aug/23 $$\mathrm{Calculer}\:\underset{\:\mathrm{0}} {\int}^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} {t}}{\:\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}{dt} \\ $$ Answered by witcher3 last updated on 09/Aug/23 $$\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 195278 by Erico last updated on 28/Jul/23 $$\mathrm{calculer}\:\underset{\mathrm{x}\rightarrow\pi} {\mathrm{lim}}\frac{\left(\mathrm{n}+\mathrm{1}\right)\mathrm{sin}\left(\left(\mathrm{n}−\mathrm{1}\right)\mathrm{x}\right)−\left(\mathrm{n}−\mathrm{1}\right)\mathrm{sin}\left(\left(\mathrm{n}+\mathrm{1}\right)\mathrm{x}\right)}{\mathrm{sinx}\:\mathrm{sin}\left(\mathrm{nx}\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 195087 by bett last updated on 23/Jul/23 Answered by JDamian last updated on 23/Jul/23 Answered by Rasheed.Sindhi last updated on 23/Jul/23 $$\mathrm{log}_{\mathrm{3}} \mathrm{4}{x}+\mathrm{3log}_{\mathrm{27}}…
Question Number 194961 by SirMUTUKU last updated on 20/Jul/23 Answered by mahdipoor last updated on 20/Jul/23 $${log}\mathrm{225}={log}\left(\mathrm{25}×\mathrm{9}\right)={log}\frac{\mathrm{100}}{\mathrm{4}}+{log}\mathrm{9}= \\ $$$${log}\mathrm{100}−{log}\mathrm{4}+\mathrm{2}{log}\mathrm{3}=\mathrm{2}−.\mathrm{6021}+\mathrm{2}×.\mathrm{4771}= \\ $$$$\mathrm{2}.\mathrm{3521} \\ $$ Terms of…
Question Number 194613 by cortano12 last updated on 11/Jul/23 $$\:\:\:\:\:\:\cancel{\underline{ }} \\ $$ Answered by MM42 last updated on 11/Jul/23 $$\frac{\mathrm{1}}{{log}_{{x}} \mathrm{4}{x}}+\frac{\mathrm{1}}{{log}_{{x}} \frac{{x}}{\mathrm{2}}}=\mathrm{2} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}{log}_{{x}}…