Question Number 165550 by mnjuly1970 last updated on 03/Feb/22 Answered by mahdipoor last updated on 03/Feb/22 $${f}\left(\mathrm{1}\right)=\sqrt{\mathrm{11}}\:,\:{f}\left({f}\left(\mathrm{1}\right)\right)=\sqrt{\mathrm{22}}\:,\:{f}\left({f}\left({f}\left(\mathrm{1}\right)\right)\right)=\sqrt{\mathrm{33}} \\ $$$$…\:{f}\left({f}…{f}\left(\mathrm{1}\right)…\right)=\sqrt{\mathrm{10}{n}+\mathrm{1}} \\ $$$$\Rightarrow{f}'\left({x}\right)=\frac{{x}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{10}}} \\ $$$${f}'\left(\mathrm{1}\right)×{f}\left(\sqrt{\mathrm{11}}\right)×{f}\left(\sqrt{\mathrm{22}}\right)×…×{f}\left(\sqrt{\mathrm{10}{n}+\mathrm{1}}\right)= \\…
Question Number 34421 by abdo mathsup 649 cc last updated on 06/May/18 $${let}\:{A}\:\:=\:\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{dx}}{{x}^{\mathrm{2}} \:−{j}}\:\:\:\:{with}\:{j}={e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{3}}} \\ $$$${extract}\:\:{ReA}\:{and}\:{Im}\left({A}\right)\:{and}\:{calculste}\:{its}\:{values}. \\ $$ Commented by abdo mathsup 649…
Question Number 165426 by mnjuly1970 last updated on 01/Feb/22 $$ \\ $$$$\:\:\:\:{prove}\:\:{that} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\zeta\:\left(\mathrm{0}\:\right)=\:\frac{−\mathrm{1}}{\mathrm{2}}\:\:\: \\ $$$$ \\ $$ Commented by abdullahoudou last updated…
Question Number 165418 by mnjuly1970 last updated on 01/Feb/22 $$ \\ $$$$\:\:\:\:\:{prove}\:\:{that}\:: \\ $$$$ \\ $$$$\:\:\:\mathrm{1}^{\ast} :\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\zeta\:\left(\mathrm{2}{n}\:\right)−\mathrm{1}}{\:\mathrm{1}+\:{n}}\:=\:\frac{\mathrm{3}}{\mathrm{2}\:}\:\:−\:\mathrm{ln}\:\left(\pi\:\right) \\ $$$$\:\:\:\mathrm{2}^{\:\ast\ast} :\:\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\:\left(−\mathrm{1}\right)^{\:{n}} \left(\:\:\zeta\:\left({n}\:\right)−\mathrm{1}\:\right)}{\mathrm{1}\:+\:{n}}=\frac{\mathrm{3}}{\mathrm{2}}\:+\frac{\gamma}{\mathrm{2}}\:−\frac{\mathrm{ln}\left(\mathrm{8}\pi\right)}{\mathrm{2}}…
Question Number 34320 by abdo mathsup 649 cc last updated on 04/May/18 $${calculate}\:\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\frac{{dx}}{{x}^{\mathrm{2}} \:+\mathrm{1}\:−{i}} \\ $$ Commented by math khazana by abdo last…
Question Number 34316 by prof Abdo imad last updated on 03/May/18 $${find}\:{a}\:{eajivalent}\:{of} \\ $$$${u}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:{e}^{−\frac{{t}}{{n}}} \:\:\:{arcctant}\:{dt}\:. \\ $$ Terms of Service Privacy Policy…
Question Number 34315 by prof Abdo imad last updated on 03/May/18 $$\left.\mathrm{1}\right)\:{find}\:\:{F}\left({x}\right)=\:\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{e}^{−{at}} \:−{e}^{−{bt}} }{{t}}{sin}\left({xt}\right){dt} \\ $$$${with}\:{a}>\mathrm{0}\:,{b}>\mathrm{0}\:. \\ $$ Commented by math khazana by…
Question Number 34314 by prof Abdo imad last updated on 03/May/18 $${let}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{+\infty} \:\:\frac{\mathrm{1}−{cos}\left({xt}\right)}{{t}^{\mathrm{2}} }\:{e}^{−{t}} {dt}\: \\ $$$${calculate}\:{f}\left({x}\right)\:. \\ $$ Commented by prof Abdo imad…
Question Number 34312 by prof Abdo imad last updated on 03/May/18 $${calculate}\:{I}\:\:=\:\int\int_{{D}} {x}^{\mathrm{3}} {dxdy}\:\:\:{on}\:{the}\:{domain} \\ $$$${D}\:=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\mathrm{1}\leqslant{x}\leqslant\mathrm{2}\:,\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} −\mathrm{1}\geqslant\mathrm{0}\right\} \\ $$ Commented by math khazana…
Question Number 165380 by mnjuly1970 last updated on 31/Jan/22 $$ \\ $$$$\:\:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\:{x}^{\:\mathrm{3}} }{{sin}^{\:\mathrm{2}} \left({x}\right)}{dx}\overset{?} {=}\:\frac{\mathrm{3}}{\mathrm{8}}\:\left(\pi^{\:\mathrm{2}} {ln}\left(\mathrm{4}\right)−\mathrm{7}\zeta\left(\mathrm{3}\right)\right) \\ $$ Answered by Ar Brandon last…