Question Number 172323 by Giantyusuf last updated on 25/Jun/22 $${which}\:{number}\:{is}\:{greater} \\ $$$$\mathrm{22}^{\mathrm{55}} \:\boldsymbol{{and}}\:\mathrm{55}^{\mathrm{22}} \:??? \\ $$ Answered by nurtani last updated on 25/Jun/22 $$\mathrm{22}^{\mathrm{55}} \:>\:\mathrm{55}^{\mathrm{22}}…
Question Number 172312 by naka3546 last updated on 25/Jun/22 $${x}\:+\:\frac{\mathrm{2}}{{x}}\:=\:\mathrm{2}{y} \\ $$$${y}\:+\:\frac{\mathrm{2}}{{y}}\:=\:\mathrm{2}{z} \\ $$$${z}\:+\:\frac{\mathrm{2}}{{z}}\:=\:\mathrm{2}{x} \\ $$$$\left({x},\:{y},\:{z}\right)\:=\:? \\ $$ Commented by MJS_new last updated on 25/Jun/22…
Question Number 172309 by mathocean1 last updated on 25/Jun/22 $${Determinate}\: \\ $$$$\underset{{n}\rightarrow+\infty} {{lim}}\left(\sum_{{k}=\mathrm{1}} ^{{n}} \frac{\left(−\mathrm{1}\right)^{{k}+\mathrm{1}} }{{k}}\right) \\ $$ Commented by mr W last updated on…
Question Number 172311 by mathocean1 last updated on 25/Jun/22 $${Using}\:{Riemann}'{s}\:{sum},\:{calculate}: \\ $$$${lim}\:{b}_{{n}} =\frac{\mathrm{1}}{{n}}\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} {cos}\mathrm{2}\left(\frac{{kn}}{{n}}\right) \\ $$ Commented by JDamian last updated on 25/Jun/22 $$!!!\:\:\frac{{k}\cancel{{n}}}{\cancel{{n}}}={k}…
Question Number 172304 by mathocean1 last updated on 25/Jun/22 $${study}\:{the}\:{convergence}\:{of}: \\ $$$${I}\left(\alpha\right)=\int_{\mathrm{1}} ^{\alpha} \frac{\mathrm{1}}{{t}^{\alpha} \left(\sqrt{{t}^{\mathrm{2}} −\mathrm{1}}\right)}{dt},\:{in}\:{function}\: \\ $$$${of}\:{real}\:\alpha. \\ $$$${Calculate}\:{I}\left(\alpha\right)\:{for}\:\alpha=\mathrm{1};\mathrm{2};\mathrm{4}.\: \\ $$ Terms of Service…
Question Number 172307 by mathocean1 last updated on 25/Jun/22 $${Calculate}\: \\ $$$$\underset{{n}\rightarrow+\infty} {{lim}A}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{{n}} }{\mathrm{1}+{x}}{dx} \\ $$ Answered by aleks041103 last updated on…
Question Number 172306 by mathocean1 last updated on 25/Jun/22 $${show}\:{that}\:{J}=\int_{\mathrm{0}} ^{+\infty} \frac{{ln}\left({t}\right)}{{t}^{\mathrm{2}} +{a}^{\mathrm{2}} }{dt}\:{with}\:{a}>\mathrm{0} \\ $$$${is}\:{convergent} \\ $$ Answered by aleks041103 last updated on 25/Jun/22…
Question Number 106743 by mohammad17 last updated on 06/Aug/20 $$\int\sqrt{{secy}}{dy} \\ $$ Answered by Sarah85 last updated on 07/Aug/20 $$\int\sqrt{\mathrm{sec}\:{y}}{dy}=\int\frac{{dy}}{\:\sqrt{\mathrm{cos}\:{y}}}=\int\frac{{dy}}{\:\sqrt{\mathrm{1}−\mathrm{2sin}^{\mathrm{2}} \:\frac{{y}}{\mathrm{2}}}} \\ $$$$\mathrm{let}\:{t}=\frac{{y}}{\mathrm{2}} \\ $$$$\mathrm{2}\int\frac{{dt}}{\:\sqrt{\mathrm{1}−\mathrm{2sin}^{\mathrm{2}}…
Question Number 41198 by mondodotto@gmail.com last updated on 03/Aug/18 $$\mathrm{evaluate}\:\boldsymbol{\mathrm{ln}}\left(−\mathrm{1}\right) \\ $$ Commented by math khazana by abdo last updated on 03/Aug/18 $${we}\:\:{have}\:\:−\mathrm{1}\:={e}^{{i}\left(\mathrm{2}{k}+\mathrm{1}\right)\pi} \:\:\:\:\:\forall{k}\in{Z}\:\Rightarrow \\…
Question Number 106726 by ZiYangLee last updated on 06/Aug/20 $$\mathrm{Prove}\:\mathrm{sin5}\theta=\mathrm{16sin}^{\mathrm{5}} \theta−\mathrm{20sin}^{\mathrm{3}} \theta+\mathrm{5sin}\theta \\ $$$$\mathrm{Hence},\:\mathrm{show}\:\mathrm{that}\:\mathrm{sin}\:\mathrm{6}°\:\mathrm{is}\:\mathrm{an} \\ $$$$\mathrm{irrational}\:\mathrm{number}.\: \\ $$ Answered by Ar Brandon last updated on…