Question Number 1963 by 123456 last updated on 26/Oct/15 $${f}:\left[\mathrm{0},+\infty\right)\rightarrow\mathbb{R},{a}:\mathbb{N}\rightarrow\mathbb{R} \\ $$$${a}_{{n}+\mathrm{1}} ={f}\left({a}_{{n}} \right)−{a}_{{n}} \\ $$$${f}\left({x}\right)\geqslant{f}\left({y}\right),\forall{x}\geqslant{y}\geqslant\mathrm{0} \\ $$$$\mathrm{does} \\ $$$${a}_{{n}} \geqslant{a}_{{m}} ,\forall{n}\geqslant{m}\geqslant\mathrm{0}? \\ $$ Answered…
Question Number 1956 by 123456 last updated on 26/Oct/15 $${x}_{{n}+\mathrm{1}} ={y}_{{n}} −\mathrm{1} \\ $$$${y}_{{n}+\mathrm{1}} ={x}_{{n}} +\mathrm{1} \\ $$$${x}_{\mathrm{0}} =\mathrm{1},{y}_{\mathrm{0}} =\mathrm{1} \\ $$$${x}_{\mathrm{10}} +{y}_{\mathrm{10}} =? \\…
Question Number 67461 by mathmax by abdo last updated on 27/Aug/19 $${find}\:{the}\:{value}\:{of}\:\sum_{{p}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{p}} }{\left(\mathrm{2}{p}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 1873 by 123456 last updated on 19/Oct/15 $${f}_{{n}+\mathrm{1}} \left({x}\right)={f}_{{n}} \left({x}\right)\left({x}−{n}\right)\left({x}+{n}\right) \\ $$$${f}_{\mathrm{0}} \left({x}\right)=\mathrm{1} \\ $$$${f}_{\mathrm{5}} \left({x}\right)=? \\ $$$${f}_{\mathrm{4}} \left(\mathrm{2}{x}\right)=\mathrm{0},{x}=? \\ $$ Answered by…
Question Number 132932 by bobhans last updated on 17/Feb/21 $${Find}\:{f}\left({x}\right)\:{such}\:{that}\:{f}\left(\mathrm{2}{x}\right)={f}\left({x}\right) \\ $$ Answered by Olaf last updated on 17/Feb/21 $${f}\left(\mathrm{2}{x}\right)\:=\:{f}\left({x}\right) \\ $$$$\Rightarrow\:{f}\left({x}\right)\:=\:{f}\left(\frac{{x}}{\mathrm{2}}\right)\:=\:{f}\left(\frac{{x}}{\mathrm{4}}\right)\:=\:…{f}\left(\frac{{x}}{\mathrm{2}^{{n}} }\right)… \\ $$$${f}\left({x}\right)\:=\:\underset{{n}\rightarrow\infty}…
Question Number 132935 by liberty last updated on 17/Feb/21 Answered by EDWIN88 last updated on 17/Feb/21 $$\:\mathrm{let}\:\mathrm{x}=\mathrm{2}\:\Rightarrow\:\mathrm{f}\left(\mathrm{2}\right).\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)=\mathrm{f}\left(\mathrm{2}\right)+\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$$$\Rightarrow\:\mathrm{65}.\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\:=\:\mathrm{65}+\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$$$\Rightarrow\:\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\:=\:\frac{\mathrm{65}}{\mathrm{64}}\:\Rightarrow\:\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)=\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{64}} \\ $$$$\Rightarrow\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\:=\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{6}} }\:\Rightarrow\mathrm{f}\left(\mathrm{x}\right)=\mathrm{1}+\mathrm{x}^{\mathrm{6}} \\…
Question Number 67384 by mathmax by abdo last updated on 26/Aug/19 $${find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{cos}\left({nx}\right)}{{n}^{\mathrm{2}} } \\ $$ Commented by mathmax by abdo last updated on…
Question Number 67381 by mathmax by abdo last updated on 26/Aug/19 $${let}\:{f}\left({x}\right)\:={x}^{\mathrm{2}} \:\:\:\:\:\:\:\mathrm{2}\pi\:{periodic}\:\:{even}\:\:{develop}\:{f}\:{at}\:{fourier}\:{serie} \\ $$ Commented by mathmax by abdo last updated on 27/Aug/19 $${f}\:{even}\:\Rightarrow{f}\left({x}\right)\:=\frac{{a}_{\mathrm{0}}…
Question Number 67380 by mathmax by abdo last updated on 26/Aug/19 $${solve}\:{the}\:\left({d}.{e}.\right)\:\:\:\:\left(\:{x}^{\mathrm{2}} −{x}+\mathrm{1}\:\:\:\:\:\:\right){y}^{'} −\left(\mathrm{2}{x}+\mathrm{3}\right){y}\:={x}^{\mathrm{2}} \:{e}^{{x}} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 67378 by mathmax by abdo last updated on 26/Aug/19 $${let}\:{f}\left({x}\right)\:={x}^{\mathrm{3}} \:\:\:\:\:\:,\mathrm{2}\pi\:{periodic}\:{odd} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie}\: \\ $$ Commented by mathmax by abdo last updated on…