Question Number 54675 by maxmathsup by imad last updated on 09/Feb/19 $${simplify}\:\:{A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}^{\mathrm{2}} \:{C}_{{n}} ^{{k}} \:{cos}\left({k}\theta\right)\:{and}\:{B}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}^{\mathrm{2}} \:{C}_{{n}} ^{{k}} \:{sin}\left({k}\theta\right)\:. \\…
Question Number 185678 by Mingma last updated on 25/Jan/23 Answered by Frix last updated on 25/Jan/23 $${y}^{\mathrm{3}} +\mathrm{2}{y}−{x}=\mathrm{0} \\ $$$$\mathrm{Cardano}'\mathrm{s}\:\mathrm{Formula} \\ $$$${y}=\sqrt[{\mathrm{3}}]{\frac{{x}}{\mathrm{2}}+\sqrt{\frac{{x}^{\mathrm{2}} }{\mathrm{4}}+\frac{\mathrm{8}}{\mathrm{27}}}}−\sqrt[{\mathrm{3}}]{−\frac{{x}}{\mathrm{2}}+\sqrt{\frac{{x}^{\mathrm{2}} }{\mathrm{4}}+\frac{\mathrm{8}}{\mathrm{27}}}} \\…
Question Number 54504 by afachri last updated on 05/Feb/19 $$\boldsymbol{\mathrm{please}},\boldsymbol{\mathrm{Sir}}.\:\:\:\boldsymbol{\mathrm{Would}}\:\boldsymbol{\mathrm{u}}\:\boldsymbol{\mathrm{explain}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{me}}\:\boldsymbol{\mathrm{how}}\:? \\ $$$$\boldsymbol{\mathrm{if}}\:\:\boldsymbol{{f}}\left(\frac{\boldsymbol{{x}}}{\boldsymbol{{x}}\:−\:\mathrm{1}}\right)\:\:+\:\:\mathrm{2}\boldsymbol{{f}}\left(\frac{\boldsymbol{{x}}\:−\:\mathrm{1}}{\boldsymbol{{x}}}\right)\:\:=\:\:\frac{\boldsymbol{{x}}}{\boldsymbol{{x}}\:−\:\mathrm{1}}\:\:\:, \\ $$$$\boldsymbol{\mathrm{then}}\:\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\:\:\boldsymbol{\mathrm{is}}\:…. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 05/Feb/19 $${f}\left({a}\right)+\mathrm{2}{f}\left(\frac{\mathrm{1}}{{a}}\right)={a}\:×\mathrm{2} \\…
Question Number 119909 by bramlexs22 last updated on 28/Oct/20 $${Given}\:{f}\left({x}\right)=\frac{{px}+{q}}{{x}+\mathrm{2}}\:,\:{q}\neq\:\mathrm{0} \\ $$$${f}^{−\mathrm{1}} \:\left({q}\right)\:=\:−\mathrm{1}\:{then}\:{f}^{−\mathrm{1}} \left(\mathrm{2}{q}\right)=? \\ $$ Answered by TITA last updated on 28/Oct/20 $${q}={f}\left(−\mathrm{1}\right)\:\:\:\:\:{q}={q}−{p}\:\:{p}=\mathrm{0} \\…
Question Number 54369 by maxmathsup by imad last updated on 02/Feb/19 $${find}\:{lim}_{{x}\rightarrow\mathrm{1}} \:\left(\xi\left({x}\right)−\frac{\mathrm{1}}{{x}−\mathrm{1}}\right) \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 03/Feb/19 $${what}\:{is}\:\xi\left({x}\right)… \\ $$…
Question Number 185423 by alcohol last updated on 21/Jan/23 $$\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{3}^{{r}−\mathrm{1}} {sin}^{\mathrm{3}} \left(\frac{\theta}{\mathrm{3}^{{r}} }\right)\:=\:? \\ $$ Answered by witcher3 last updated on 21/Jan/23 $$\mathrm{sin}^{\mathrm{3}}…
Question Number 119837 by mathmax by abdo last updated on 27/Oct/20 $$\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\:\:\int_{\mathrm{0}} ^{\sqrt{\mathrm{n}}} \left(\mathrm{1}−\frac{\mathrm{x}}{\:\sqrt{\mathrm{n}}}\right)^{\sqrt{\mathrm{2n}}} \:\mathrm{arctan}\left(\frac{\pi\mathrm{x}}{\mathrm{n}}\right)\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 119815 by bemath last updated on 27/Oct/20 $${Given}\:{f}\left({x}+{y}\right)=\mathrm{4}{f}\left({x}\right).{f}\left({y}\right)\:{for} \\ $$$${all}\:{real}\:{numbers}\:{x}\:{and}\:{y}. \\ $$$${If}\:{f}\left(\mathrm{3}\right)=\mathrm{32}\:{then}\:{f}\left(\mathrm{1}\right)=\_ \\ $$ Answered by Olaf last updated on 27/Oct/20 $${f}\left(\mathrm{1}+\mathrm{1}\right)\:=\:\mathrm{4}{f}\left(\mathrm{1}\right){f}\left(\mathrm{1}\right) \\…
Question Number 119754 by Bird last updated on 26/Oct/20 $${find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{u}_{{n}} }{{n}!}\:{if}\:\:{u}_{{n}} \:={u}_{{n}+\mathrm{1}} +{u}_{{n}−\mathrm{1}} \\ $$ Commented by Dwaipayan Shikari last updated on 26/Oct/20…
Question Number 185211 by Rupesh123 last updated on 18/Jan/23 Answered by manolex last updated on 18/Jan/23 $${x} \\ $$$$ \\ $$ Answered by manolex last…