Question Number 45080 by turbo msup by abdo last updated on 08/Oct/18 $${find}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{4}} } \\ $$ Commented by maxmathsup by imad last updated…
Question Number 110456 by bobhans last updated on 29/Aug/20 $$\:\:\:{If}\:\left({f}\left({x}\right).{g}\left({x}\right)\right)'\:=\:{f}\left({x}\right)'\:.\:{g}\left({x}\right)'\: \\ $$$$\:{find}\:{the}\:{function}\:{of}\:{f}\left({x}\right)\:. \\ $$ Answered by bemath last updated on 29/Aug/20 $$\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{f}\left(\mathrm{x}\right).\mathrm{g}\left(\mathrm{x}\right)\right)=\mathrm{f}\left(\mathrm{x}\right)'.\mathrm{g}\left(\mathrm{x}\right)+\mathrm{f}\left(\mathrm{x}\right).\mathrm{g}\left(\mathrm{x}\right)' \\ $$$$\mathrm{then}\:\mathrm{given}\:\mathrm{condition}\: \\…
Question Number 110449 by mathmax by abdo last updated on 29/Aug/20 $$\mathrm{find}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\frac{\mathrm{arctan}\left(\mathrm{x}−\mathrm{sinx}\right)−\mathrm{arctan}\left(\mathrm{1}−\mathrm{cosx}\right)}{\mathrm{x}^{\mathrm{2}} } \\ $$ Answered by bemath last updated on 29/Aug/20 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}−\mathrm{sin}\:\mathrm{x}−\left(\mathrm{1}−\mathrm{cos}\:\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}}…
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Question Number 110306 by Lekhraj last updated on 28/Aug/20 Commented by mr W last updated on 28/Aug/20 $${f}\left({x}\right)=\frac{\mathrm{1}\pm\sqrt{\mathrm{5}}}{\mathrm{2}}{x} \\ $$ Commented by Lekhraj last updated…
Question Number 110281 by 675480065 last updated on 28/Aug/20 Answered by Rio Michael last updated on 28/Aug/20 $$\:\mathrm{3}{x}\:\equiv\:\mathrm{1}\:\left(\mathrm{mod}\:\mathrm{5}\right)\:\:\:\:\left({i}\right) \\ $$$$\:\mathrm{5}{x}\:\equiv\:\mathrm{2}\:\left(\mathrm{mod}\:\mathrm{7}\right)\:\:\:\:\:\left({ii}\right) \\ $$$$\mathrm{from}\:\left({i}\right)\:\:{x}\:\equiv\:\mathrm{2}\:\left(\mathrm{mod}\:\mathrm{5}\right)\:\:\left({iii}\right) \\ $$$$\mathrm{from}\:\left({ii}\right)\:{x}\:\equiv\:\mathrm{6}\:\left(\mathrm{mod}\:\mathrm{7}\right)\:\:\left({iv}\right) \\…
Question Number 175801 by Lekhraj last updated on 07/Sep/22 $${solve}\:{the}\:{follwing}\:{equation} \\ $$$${x}\sqrt{{x}\:}\:\:\:+\:\:{y}\sqrt{{y}\:}\:\:=\:\:\mathrm{3}\:\:\:{and}\:\:\:{x}\sqrt{{y}\:}\:\:+\:{y}\sqrt{{x}\:}\:\:=\:\:\mathrm{2} \\ $$$${someone}\:{solve}\:{the}\:{above}\:{equations}\:{in}\:{the}\:{following}\:{way}\: \\ $$$${x}^{\mathrm{3}} +\:{y}^{\mathrm{3}} +\:\mathrm{2}{xy}\sqrt{{xy}\:}\:\:=\:\mathrm{9}…..\left(\mathrm{1}\right)\:\:\:\:{and}\:\:\:{x}^{\mathrm{2}} {y}\:\:+\:\:{y}^{\mathrm{2}} {x}\:\:+\:\mathrm{2}{xy}\sqrt{{xy}\:}\:\:=\:\:\mathrm{4}……\left(\mathrm{2}\right) \\ $$$$\left(\mathrm{1}\right)\:−\:\left(\mathrm{2}\right)\:\:\:\Rightarrow\:\:\left({x}\:−\:{y}\right)\left({x}^{\mathrm{2}} \:−\:{y}^{\mathrm{2}} \:\right)\:=\:\mathrm{5} \\…
Question Number 175780 by infinityaction last updated on 06/Sep/22 $$\:\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function} \\ $$$$\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{cosx}\left\{\mathrm{sin}{x}\:+\:\sqrt{\mathrm{sin}^{\mathrm{2}} {x}\:+\:\mathrm{sin}^{\mathrm{2}} \alpha\:\:}\:\right\}\:\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 175674 by infinityaction last updated on 05/Sep/22 Answered by mr W last updated on 05/Sep/22 $$−\frac{{b}}{\mathrm{2}{a}}=\mathrm{2}\:\Rightarrow{b}=−\mathrm{4}{a} \\ $$$${f}\left(\mathrm{2}\right)=\mathrm{4}{a}+\mathrm{2}{b}+{c}={c}−\mathrm{4}{a} \\ $$$${f}\left(\mathrm{1}\right)={a}+{b}+{c}={c}−\mathrm{3}{a}={f}\left(\mathrm{3}\right) \\ $$$${f}\left({f}\left(\mathrm{1}\right)\right)={f}\left({f}\left(\mathrm{2}\right)\right) \\…
Question Number 44468 by maxmathsup by imad last updated on 29/Sep/18 $${let}\:{u}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{{e}^{−{k}} }{\:\sqrt{{k}}} \\ $$$${find}\:{a}\:{equivalent}\:{of}\:{u}_{{n}} \:{when}\:{n}\rightarrow+\infty\:. \\ $$ Terms of Service Privacy…