Question Number 70361 by mind is power last updated on 03/Oct/19 $${Hello}\: \\ $$$${si}\left({x}\right)=−\int_{{x}} ^{\infty} \frac{{sin}\left({x}\right)}{{x}}{dx} \\ $$$${show}\:\int_{\mathrm{0}} ^{+\infty} {x}^{{a}−\mathrm{1}} {si}\left({x}\right){dx}=−\frac{\Gamma\left({a}\right){sin}\left(\frac{\pi{a}}{\mathrm{2}}\right)}{{a}} \\ $$$${hint}\:{ipp}\:+{complex}\:{Analysis} \\ $$…
Question Number 135892 by mathmax by abdo last updated on 16/Mar/21 $$\left.\mathrm{1}\right)\mathrm{decompose}\:\mathrm{inside}\:\mathrm{R}\left(\mathrm{x}\right)\:\mathrm{the}\:\mathrm{fraction}\:\mathrm{F}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{3}} \left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{4}} } \\ $$$$\left.\mathrm{2}\right)\:\mathrm{calculate}\:\int_{\mathrm{2}} ^{\infty} \:\mathrm{F}\left(\mathrm{x}\right)\mathrm{dx} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{calculate}\:\int_{\mathrm{2}} ^{\infty} \:\mathrm{F}^{\mathrm{2}} \left(\mathrm{x}\right)\mathrm{dx} \\ $$…
Question Number 4822 by FilupSmith last updated on 16/Mar/16 $$\mathrm{Can}\:\mathrm{you}\:\mathrm{please}\:\mathrm{mathematically}\:\mathrm{explain} \\ $$$$\mathrm{how}\:\mathrm{some}\:\mathrm{infinities}\:\mathrm{can}\:\mathrm{be}\:\mathrm{bigger}\:\mathrm{than} \\ $$$$\mathrm{others}?\:\mathrm{Thank}\:\mathrm{you}! \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 135895 by liberty last updated on 16/Mar/21 $${Trigonometry} \\ $$If sin A + sin B = a and cos A + cos B…
Question Number 4820 by love math last updated on 16/Mar/16 $${y}={f}\left({x}\right)+{g}\left({x}\right) \\ $$$$ \\ $$$${f}\left({x}\right)\:−\:{odd}\:{function} \\ $$$${g}\left({x}\right)\:−\:{even}\:{function} \\ $$$$ \\ $$$${find}\:{f}\left(\mathrm{0}\right),\:{if}\:{y}=\:\mathrm{2}{x}^{\mathrm{2}} +\frac{{sin}\:{x}}{\mathrm{3}}+\mathrm{1} \\ $$ Answered…
Question Number 135889 by Ar Brandon last updated on 16/Mar/21 $$\mathrm{1}\backslash\:\mathrm{If}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{sets}\:\mathrm{define}\:\mathrm{their}\:\mathrm{scheffer}\:\mathrm{product}\:\mathrm{A}\ast\mathrm{B}\:\mathrm{by}\:\mathrm{A}\ast\mathrm{B}=\mathrm{A}\ast\cap\mathrm{B}\ast \\ $$$$\mathrm{Prove}\:\mathrm{by}\:\mathrm{definitions}\:\mathrm{that}\:\left(\mathrm{A}\ast\mathrm{B}\right)\ast\left(\mathrm{A}\ast\mathrm{B}\right)=\mathrm{A}\cup\mathrm{B} \\ $$$$ \\ $$$$\mathrm{2}\backslash\:\mathrm{State}\:\mathrm{the}\:\mathrm{strong}\:\mathrm{principle}\:\mathrm{of}\:\mathrm{mathematical}\:\mathrm{induction}. \\ $$$$\mathrm{Suppose}\:\mathrm{that}\:\mathrm{a}_{\mathrm{1}} =\mathrm{1}\:,\:\mathrm{a}_{\mathrm{2}} =\mathrm{3} \\ $$$$\mathrm{a}_{\mathrm{k}} =\mathrm{a}_{\mathrm{k}−\mathrm{2}} +\mathrm{2a}_{\mathrm{k}−\mathrm{1}}…
Question Number 135888 by mnjuly1970 last updated on 16/Mar/21 Answered by mindispower last updated on 19/Mar/21 $${recal}\:\chi_{\mathrm{2}} \left({x}\right)=\frac{{li}_{\mathrm{2}} \left({x}\right)−{li}_{\mathrm{2}} \left(−{x}\right)}{\mathrm{2}},{chi}\:{function} \\ $$$${we}\:{have}\:\chi_{\mathrm{2}} \left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right)+\chi_{\mathrm{2}} \left({x}\right)=\frac{\pi^{\mathrm{2}} }{\mathrm{8}}+\frac{{ln}\left({x}\right){ln}\left(\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}\right)}{\mathrm{2}}…
Question Number 4817 by 123456 last updated on 15/Mar/16 $${f}\left(\alpha{x}\right)=\alpha{f}\left({x}−\alpha\right) \\ $$$${f}\left({x}\right)=? \\ $$ Commented by prakash jain last updated on 15/Mar/16 $${x}=\mathrm{0} \\ $$$$\mathrm{Trivial}\:\mathrm{solution}\:\mathrm{satisfies}\:\mathrm{the}\:\mathrm{equation}\:{f}\left({x}\right)=\mathrm{0}…
Question Number 4816 by Kelvin last updated on 15/Mar/16 Commented by prakash jain last updated on 15/Mar/16 $$\mathrm{log}\:.\mathrm{006}−\mathrm{log}\:.\mathrm{0012}=\mathrm{log}\:\frac{.\mathrm{006}}{.\mathrm{0012}}=\mathrm{log}\:\frac{\mathrm{60}}{\mathrm{12}}=\mathrm{log}\:\mathrm{5} \\ $$$$\mathrm{log}\:.\mathrm{007}−\mathrm{log}\:.\mathrm{00243}=\mathrm{log}\:\frac{.\mathrm{007}}{.\mathrm{00243}}=\mathrm{log}\:\frac{\mathrm{700}}{\mathrm{243}} \\ $$$$\mathrm{log}\:.\mathrm{008}+\mathrm{log}\:\mathrm{4000}=\mathrm{log}\:\left(.\mathrm{008}×\mathrm{4000}\right)=\mathrm{log}\:\mathrm{32}=\mathrm{5log}\:\mathrm{2} \\ $$$$\mathrm{log}\:.\mathrm{0128}=\mathrm{7log}\:\mathrm{2}−\mathrm{log}\:\mathrm{10000}=\mathrm{7log}\:\mathrm{2}−\mathrm{4} \\…
Question Number 135884 by Dwaipayan Shikari last updated on 16/Mar/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{H}_{{n}} ^{\left(\mathrm{7}\right)} }{{n}^{\mathrm{2}} }−\frac{{H}_{{n}} ^{\left(\mathrm{7}\right)} }{\left({n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}^{{m}} }={H}_{{n}} ^{\left({m}\right)}…