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…
Question Number 56828 by maxmathsup by imad last updated on 24/Mar/19 $${study}\:{the}\:{convergence}\:{of}\:{u}_{{n}+\mathrm{1}} =\mathrm{2}\sqrt{\mathrm{1}+{u}_{{n}} ^{\mathrm{2}} }−{u}_{{n}} −\mathrm{1}\:\:\:\:{with}\:{u}_{\mathrm{0}} =\mathrm{0} \\ $$ Commented by maxmathsup by imad last…
Question Number 56813 by maxmathsup by imad last updated on 24/Mar/19 $${study}\:{the}\:{sequence}\:\:{U}_{{n}+\mathrm{1}} =\sqrt{\frac{\mathrm{1}+{u}_{{n}} }{\mathrm{2}}} \\ $$$${with}\:{U}_{\mathrm{0}} ={a}>\mathrm{0}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 122337 by benjo_mathlover last updated on 15/Nov/20 $$\:{Find}\:{domain}\:{of}\:{function} \\ $$$$\:{r}\left({x}\right)\:=\:\mathrm{arc}\:\mathrm{cos}\:\:\left(\frac{\mathrm{3}}{\mathrm{4}+\mathrm{2sin}\:{x}}\right) \\ $$ Commented by liberty last updated on 16/Nov/20 $$\mathrm{The}\:\mathrm{function}\:\mathrm{defined}\:\mathrm{for}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x} \\ $$$$\mathrm{for}\:\mathrm{which}\:−\mathrm{1}\leqslant\:\frac{\mathrm{3}}{\mathrm{4}+\mathrm{2sin}\:\mathrm{x}}\:\leqslant\:\mathrm{1}\:. \\…