Question Number 46962 by hassentimol last updated on 03/Nov/18 Commented by hassentimol last updated on 03/Nov/18 $$ \\ $$$$\mathrm{Could}\:\mathrm{you}\:\mathrm{please}\:\mathrm{explain}\:\mathrm{me}\:\mathrm{formula}\:\left(\mathrm{8}\right)\:? \\ $$$$\mathrm{I}\:\mathrm{would}\:\mathrm{like}\:\mathrm{to}\:\mathrm{know}\:\mathrm{what}\:\mathrm{is}\:{s}\:\mathrm{and}\:{m}\:? \\ $$$$\mathrm{If}\:\mathrm{you}\:\mathrm{could}\:\mathrm{also},\:\mathrm{please}\:\mathrm{tell}\:\mathrm{me}\:\mathrm{why}\:\mathrm{is}\:\mathrm{this} \\ $$$$\mathrm{formula}\:\mathrm{for}\:?\:\mathrm{and}\:\mathrm{what}\:\mathrm{represents}\:\mathrm{its}\:\mathrm{answer}\:?…
Question Number 112492 by mathdave last updated on 08/Sep/20 $${evaluate} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{n}+{k}^{\mathrm{2}} } \\ $$ Answered by Ar Brandon last updated on…
Question Number 178026 by aurpeyz last updated on 12/Oct/22 Commented by som(math1967) last updated on 12/Oct/22 $$\mathrm{46} \\ $$ Commented by aurpeyz last updated on…
Question Number 112488 by mathdave last updated on 08/Sep/20 $${solve} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{4}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 112489 by mathdave last updated on 08/Sep/20 $${solve} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{ln}^{\mathrm{2}} \left(\mathrm{sin}{x}\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 112487 by mathdave last updated on 08/Sep/20 $${solve} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\left(\mathrm{1}+{x}^{\mathrm{3}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 177975 by aurpeyz last updated on 11/Oct/22 Answered by mr W last updated on 11/Oct/22 $$\angle{ACB}={x}/\mathrm{2} \\ $$$$\angle{BAC}={y} \\ $$$$\angle{B}=\mathrm{180}−{x}/\mathrm{2}−{y} \\ $$$$\angle{ADC}=\mathrm{180}−\angle{B}={x}/\mathrm{2}+{y} \\…
Question Number 112393 by ZiYangLee last updated on 07/Sep/20 $${gf}^{−\mathrm{1}} \left({x}\right)=\mathrm{3}{x}−\mathrm{2} \\ $$$${fg}\left({x}\right)=\mathrm{12}{x}−\mathrm{8} \\ $$$$ \\ $$$$\mathrm{then}\:{g}^{\mathrm{2}} \left({x}\right)=? \\ $$ Commented by ZiYangLee last updated…
Question Number 112366 by mathdave last updated on 07/Sep/20 Answered by mathmax by abdo last updated on 07/Sep/20 $$\mathrm{let}\:\mathrm{S}_{\mathrm{n}} =\mathrm{n}\:\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}−\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{k}+\mathrm{n}\right)−\mathrm{ln}\left(\mathrm{n}\right)}{\mathrm{n}^{\mathrm{2}} \:+\mathrm{k}^{\mathrm{2}} }\:\Rightarrow \\…
Question Number 112369 by mathdave last updated on 07/Sep/20 $${prove}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{tanh}{x}}{{x}^{\mathrm{3}} }−\frac{\mathrm{sech}^{\mathrm{2}} {x}}{{x}^{\mathrm{2}} }\right){dx}=\frac{\mathrm{7}}{\pi^{\mathrm{2}} }\zeta\left(\mathrm{3}\right) \\ $$$${where}\:\zeta\left(\mathrm{3}\right)={apery}'{s}\:{constant} \\ $$ Terms of Service…