Question Number 193685 by cortano12 last updated on 18/Jun/23 $$\:\:\:\:\:\:\:\left(\mathrm{f}\left(\mathrm{x}\right)\right)^{\mathrm{2}} −\mathrm{4xf}\left(\mathrm{x}\right)+\mathrm{3}=\mathrm{0} \\ $$$$\:\:\:\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{3}\right)=?\: \\ $$ Answered by mr W last updated on 18/Jun/23 $${y}^{\mathrm{2}}…
Question Number 193554 by Mingma last updated on 16/Jun/23 Answered by aba last updated on 17/Jun/23 $$\mathrm{a}=\mathrm{1}\:\wedge\:\mathrm{b}=\mathrm{0}\: \\ $$ Answered by aba last updated on…
Question Number 193267 by Mingma last updated on 09/Jun/23 Answered by cortano12 last updated on 09/Jun/23 $$\:\:\left(\mathrm{i}\right)\:\mathrm{4f}\left(\mathrm{x}\right)+\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)=\mathrm{24x}+\mathrm{5}+\frac{\mathrm{6}}{\mathrm{x}} \\ $$$$\:\:\left(\mathrm{ii}\right)\:\mathrm{4f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)+\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{24}}{\mathrm{x}}+\mathrm{5}+\mathrm{6x} \\ $$$$\:\:\left(\mathrm{i}\right)×\mathrm{4}=\:\mathrm{4f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)+\mathrm{16f}\left(\mathrm{x}\right)=\mathrm{96x}+\mathrm{20}+\frac{\mathrm{24}}{\mathrm{x}} \\ $$$$\:\:\left(\mathrm{i}\right)−\left(\mathrm{ii}\right) \\ $$$$\:\:\:\Rightarrow\mathrm{15f}\left(\mathrm{x}\right)=\mathrm{90x}+\mathrm{15}…
Question Number 131048 by mathmax by abdo last updated on 31/Jan/21 $$\mathrm{solve}\:\mathrm{y}^{''} −\mathrm{y}^{'} \:+\mathrm{y}\:=\frac{\mathrm{e}^{−\mathrm{x}} }{\mathrm{x}+\mathrm{1}} \\ $$ Answered by Ar Brandon last updated on 01/Feb/21…
Question Number 65488 by mathmax by abdo last updated on 30/Jul/19 $${U}_{{n}} {is}\:{a}\:{sequence}\:{wich}\:{verify}\:\:\forall{n}\in{N}^{\bigstar} \\ $$$${U}_{{n}} \:+{U}_{{n}+\mathrm{1}} =\frac{\mathrm{1}}{{n}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{is}\:{the}\:{sequence}\:{U}_{{n}} {convergent}? \\ $$…
Question Number 65489 by mathmax by abdo last updated on 30/Jul/19 $${U}_{{n}} \:{is}\:{a}\:{sequence}\:{wich}\:{verify}\:\:{U}_{{n}} \:+{U}_{{n}+\mathrm{1}} =\frac{\mathrm{1}}{{n}^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right)\:{find}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:{U}_{{n}} \\ $$ Commented…
Question Number 65402 by mathmax by abdo last updated on 29/Jul/19 $${solve}\:{the}\:\left({de}\right)\:\:\:\:\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}{y}^{''} \:\:\:−{xy}^{'} \:={x}^{\mathrm{2}} −{x} \\ $$ Commented by mathmax by abdo last updated…
Question Number 65403 by mathmax by abdo last updated on 29/Jul/19 $${solve}\:{the}\left({de}\right)\:\:\:\:\:\:{x}^{\mathrm{3}} {y}^{''} −\mathrm{2}{xy}^{'} \:+\left({x}+\mathrm{1}\right){y}\:=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 65386 by mathmax by abdo last updated on 29/Jul/19 $${calculate}\:\sum_{{k}=\mathrm{1}} ^{\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{k}−\mathrm{1}} }{\mathrm{99}{k}−\mathrm{1}} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 65383 by mathmax by abdo last updated on 29/Jul/19 $$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\mathrm{1}+{e}^{{nx}} }\:\:\:{with}\:{n}\:{integr}\:{natural}\:\:{and}\:{n}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{conclude}\:{the}\:{value}\:{of}\:\sum_{{k}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{k}−\mathrm{1}} }{{k}} \\ $$ Commented by mathmax…