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Question Number 172326 Answers: 2 Comments: 4
$${If}\: \\ $$$$\:\:\:\:\:\:\:\:\:\left({x}^{\mathrm{3}} +{x}^{\mathrm{2}} +{x}\right)+\left(\frac{\mathrm{1}}{{x}^{\mathrm{3}} }+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }+\frac{\mathrm{1}}{{x}}\right)\:=\:\mathrm{70} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}^{\mathrm{4}} +\frac{\mathrm{1}}{{x}^{\mathrm{4}} }\:=\:\:? \\ $$
Question Number 172323 Answers: 4 Comments: 0
$${which}\:{number}\:{is}\:{greater} \\ $$$$\mathrm{22}^{\mathrm{55}} \:\boldsymbol{{and}}\:\mathrm{55}^{\mathrm{22}} \:??? \\ $$
Question Number 172321 Answers: 0 Comments: 0
Question Number 172312 Answers: 1 Comments: 11
$${x}\:+\:\frac{\mathrm{2}}{{x}}\:=\:\mathrm{2}{y} \\ $$$${y}\:+\:\frac{\mathrm{2}}{{y}}\:=\:\mathrm{2}{z} \\ $$$${z}\:+\:\frac{\mathrm{2}}{{z}}\:=\:\mathrm{2}{x} \\ $$$$\left({x},\:{y},\:{z}\right)\:=\:? \\ $$
Question Number 172311 Answers: 0 Comments: 4
$${Using}\:{Riemann}'{s}\:{sum},\:{calculate}: \\ $$$${lim}\:{b}_{{n}} =\frac{\mathrm{1}}{{n}}\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} {cos}\mathrm{2}\left(\frac{{kn}}{{n}}\right) \\ $$
Question Number 172309 Answers: 1 Comments: 1
$${Determinate}\: \\ $$$$\underset{{n}\rightarrow+\infty} {{lim}}\left(\sum_{{k}=\mathrm{1}} ^{{n}} \frac{\left(−\mathrm{1}\right)^{{k}+\mathrm{1}} }{{k}}\right) \\ $$
Question Number 172307 Answers: 3 Comments: 0
$${Calculate}\: \\ $$$$\underset{{n}\rightarrow+\infty} {{lim}A}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{{n}} }{\mathrm{1}+{x}}{dx} \\ $$
Question Number 172306 Answers: 2 Comments: 0
$${show}\:{that}\:{J}=\int_{\mathrm{0}} ^{+\infty} \frac{{ln}\left({t}\right)}{{t}^{\mathrm{2}} +{a}^{\mathrm{2}} }{dt}\:{with}\:{a}>\mathrm{0} \\ $$$${is}\:{convergent} \\ $$
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$${study}\:{the}\:{convergence}\:{of}: \\ $$$${I}\left(\alpha\right)=\int_{\mathrm{1}} ^{\alpha} \frac{\mathrm{1}}{{t}^{\alpha} \left(\sqrt{{t}^{\mathrm{2}} −\mathrm{1}}\right)}{dt},\:{in}\:{function}\: \\ $$$${of}\:{real}\:\alpha. \\ $$$${Calculate}\:{I}\left(\alpha\right)\:{for}\:\alpha=\mathrm{1};\mathrm{2};\mathrm{4}.\: \\ $$
Question Number 172287 Answers: 0 Comments: 0
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