Question Number 57010 by 121194 last updated on 28/Mar/19 $${f}\left(\frac{{x}+{y}}{\mathrm{2}}\right)=\frac{{f}\left({x}\right){f}\left({y}\right)}{{f}\left(\mathrm{2}\right)} \\ $$$${f}\left({x}\right)=? \\ $$ Commented by maxmathsup by imad last updated on 29/Mar/19 $${x}={y}\:\Rightarrow{f}\left({x}\right)=\frac{{f}^{\mathrm{2}} \left({x}\right)}{{f}\left(\mathrm{2}\right)}\:\:{with}\:{f}\left(\mathrm{2}\right)\neq\mathrm{0}\:\Rightarrow{f}^{\mathrm{2}}…
Question Number 57011 by 121194 last updated on 28/Mar/19 $${f}\left(\frac{{x}+{y}}{\mathrm{2}}\right){f}\left(\frac{{x}−{y}}{\mathrm{2}}\right)={g}\left({x}\right) \\ $$$${g}\left({x}+{y}\right){g}\left({x}−{y}\right)=\left[{f}\left({x}\right)\right]^{\mathrm{2}} −\left[{f}\left({y}\right)\right]^{\mathrm{2}} \\ $$$${f}\left({x}\right),{g}\left({x}\right)=? \\ $$ Answered by kaivan.ahmadi last updated on 28/Mar/19 $${g}\left({x}\right)…
Question Number 56962 by turbo msup by abdo last updated on 27/Mar/19 $${find}\:{S}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}^{\mathrm{2}} \:{C}_{{n}} ^{{k}} \:{cos}\left(\mathrm{2}{kx}\right) \\ $$$${interms}\:{of}\:{n}. \\ $$ Commented by…
Question Number 56942 by maxmathsup by imad last updated on 26/Mar/19 $${find}\:\:{U}_{{n}} =\int_{\mathrm{1}} ^{{n}} \:\frac{\left[\sqrt{{x}+\mathrm{1}}\right]−\left[\sqrt{{x}}\right]}{{x}^{\mathrm{3}} }\:{dx} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:{the}\:{serie}\:\Sigma\:{U}_{{n}} \\ $$ Terms of Service Privacy Policy…
Question Number 56921 by rahul 19 last updated on 26/Mar/19 $${Given}\:: \\ $$$${f}\left({xy}\right)={f}\left({x}\right).{f}\left({y}\right)\forall{x},{y}\epsilon\mathbb{R}\:{and}\:{f}\left(\mathrm{0}\right)\neq\mathrm{0} \\ $$$${then}\:{f}\left({x}\right)=? \\ $$ Answered by mr W last updated on 26/Mar/19…
Question Number 187988 by cortano12 last updated on 24/Feb/23 $$\:\mathrm{find}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right) \\ $$$$\:\mathrm{such}\:\mathrm{that}\:\begin{cases}{\mathrm{f}\left(\mathrm{2x}−\mathrm{1}\right)+\mathrm{g}\left(\mathrm{1}−\mathrm{x}\right)=\mathrm{x}+\mathrm{1}}\\{\mathrm{f}\left(\frac{\mathrm{x}}{\mathrm{x}+\mathrm{1}}\right)+\mathrm{2g}\left(\frac{\mathrm{1}}{\mathrm{2x}+\mathrm{2}}\right)=\mathrm{3}}\end{cases} \\ $$ Answered by MathGuy last updated on 24/Feb/23 $${Answer}\::−\:{do}\:{x}\rightarrow{x}+\mathrm{1}\:{in}\:{eq}.\mathrm{1}\:\&\:{x}\rightarrow{x}−\mathrm{1}\:{in}\:{eq}.\mathrm{2} \\ $$$${you}\:{will}\:{get} \\…
Question Number 56864 by Joel578 last updated on 25/Mar/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{recurrence}\:\mathrm{relation} \\ $$$${a}_{{n}} \:=\:\mathrm{2}{a}_{{n}−\mathrm{1}} \:+\:\mathrm{3}{a}_{{n}−\mathrm{2}} ,\:\mathrm{with}\:{a}_{\mathrm{0}} \:=\:\mathrm{1},\:{a}_{\mathrm{1}} \:=\:\mathrm{2} \\ $$ Commented by maxmathsup by imad last…
Question Number 56832 by maxmathsup by imad last updated on 24/Mar/19 $${let}\:\:{Z}_{{n}} \left({x}\right)={sin}\left({narcsinx}\right)\:\:{with}\:{n}\:{integr} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{roots}\:{of}\:{Z}_{{n}} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{decompose}\:{the}\:{fraction}\:{F}\:=\frac{\mathrm{1}}{{Z}_{{n}} \left({x}\right)} \\ $$ Terms of Service Privacy…
Question Number 56830 by maxmathsup by imad last updated on 24/Mar/19 $${let}\:{A}_{{n}} =\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{cos}\left({kx}\right) \\ $$$$\:{find}\:{a}\:{simple}\:{form}\:{of}\:{A}_{{n}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 56831 by maxmathsup by imad last updated on 24/Mar/19 $${let}\:{f}\left({x}\right)\:=\sqrt{{x}^{\mathrm{2}} +\mathrm{3}}−\mathrm{2}{x}\:−\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx} \\ $$$$\left.\mathrm{2}\right){determine}\:{f}^{−\mathrm{1}} \left({x}\right)\:{and}\:{calculate}\:\int\:{f}^{−\mathrm{1}} \left({x}\right){dx}\:. \\ $$ Commented by…