Question Number 70364 by 20190927 last updated on 03/Oct/19 $$\mathrm{solve}\:\mathrm{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{e}^{\mathrm{x}} −\frac{\mathrm{1}}{\mathrm{1}−\mathrm{x}}}{\mathrm{x}^{\mathrm{2}} } \\ $$ Commented by kaivan.ahmadi last updated on 03/Oct/19 $${lim}_{{x}\rightarrow\mathrm{0}} \frac{\left(\mathrm{1}−{x}\right){e}^{{x}} −\mathrm{1}}{{x}^{\mathrm{2}}…
Question Number 70360 by Hassen_Timol last updated on 03/Oct/19 $$\underset{{n}\rightarrow+\infty} {\mathrm{l}im}\:\:\:\:\frac{\sqrt{{n}\:+\:\mathrm{1}\:}−\:{n}}{\:\sqrt{{n}\:+\:\mathrm{1}}\:+\:{n}}\:\:=\:\:? \\ $$ Answered by mind is power last updated on 03/Oct/19 $$\frac{\sqrt{{n}+\mathrm{1}}−{n}}{\:\sqrt{{n}+\mathrm{1}}+{n}}=\frac{{n}\left(\sqrt{\frac{{n}+\mathrm{1}}{{n}^{\mathrm{2}} }}−\mathrm{1}\right)}{{n}\left(\sqrt{\frac{{n}+\mathrm{1}}{{n}^{\mathrm{2}} }}+\mathrm{1}\right)}=\frac{\sqrt{\frac{\mathrm{1}}{{n}}+\frac{\mathrm{1}}{{n}^{\mathrm{2}}…
Question Number 4825 by sanusihammed last updated on 16/Mar/16 $${Find}\:{the}\:{value}\:{of}\: \\ $$$$ \\ $$$$\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}}}}}} \\ $$ Commented by prakash jain last updated on 16/Mar/16 $$\mathrm{Assuming}\:\mathrm{the}\:\mathrm{series}\:\mathrm{goes}\:\mathrm{infinitely}…
Question Number 70361 by mind is power last updated on 03/Oct/19 $${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}}…