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Question Number 172326 Answers: 2 Comments: 4

If (x^3 +x^2 +x)+((1/x^3 )+(1/x^2 )+(1/x)) = 70 x^4 +(1/x^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 22^(55) and 55^(22) ???

$${which}\:{number}\:{is}\:{greater} \\ $$$$\mathrm{22}^{\mathrm{55}} \:\boldsymbol{{and}}\:\mathrm{55}^{\mathrm{22}} \:??? \\ $$

Question Number 172321 Answers: 0 Comments: 0

Question Number 172312 Answers: 1 Comments: 11

x + (2/x) = 2y y + (2/y) = 2z z + (2/z) = 2x (x, y, z) = ?

$${x}\:+\:\frac{\mathrm{2}}{{x}}\:=\:\mathrm{2}{y} \\ $$$${y}\:+\:\frac{\mathrm{2}}{{y}}\:=\:\mathrm{2}{z} \\ $$$${z}\:+\:\frac{\mathrm{2}}{{z}}\:=\:\mathrm{2}{x} \\ $$$$\left({x},\:{y},\:{z}\right)\:=\:? \\ $$

Question Number 172311 Answers: 0 Comments: 4

Using Riemann′s sum, calculate: lim b_n =(1/n)Σ_(k=0) ^(n−1) cos2(((kn)/n))

$${Using}\:{Riemann}'{s}\:{sum},\:{calculate}: \\ $$$${lim}\:{b}_{{n}} =\frac{\mathrm{1}}{{n}}\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} {cos}\mathrm{2}\left(\frac{{kn}}{{n}}\right) \\ $$

Question Number 172309 Answers: 1 Comments: 1

Determinate lim_(n→+∞) (Σ_(k=1) ^n (((−1)^(k+1) )/k))

$${Determinate}\: \\ $$$$\underset{{n}\rightarrow+\infty} {{lim}}\left(\sum_{{k}=\mathrm{1}} ^{{n}} \frac{\left(−\mathrm{1}\right)^{{k}+\mathrm{1}} }{{k}}\right) \\ $$

Question Number 172307 Answers: 3 Comments: 0

Calculate lim_(n→+∞) A_n =∫_0 ^1 (x^n /(1+x))dx

$${Calculate}\: \\ $$$$\underset{{n}\rightarrow+\infty} {{lim}A}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{{n}} }{\mathrm{1}+{x}}{dx} \\ $$

Question Number 172306 Answers: 2 Comments: 0

show that J=∫_0 ^(+∞) ((ln(t))/(t^2 +a^2 ))dt with a>0 is convergent

$${show}\:{that}\:{J}=\int_{\mathrm{0}} ^{+\infty} \frac{{ln}\left({t}\right)}{{t}^{\mathrm{2}} +{a}^{\mathrm{2}} }{dt}\:{with}\:{a}>\mathrm{0} \\ $$$${is}\:{convergent} \\ $$

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Question Number 172304 Answers: 0 Comments: 0

study the convergence of: I(α)=∫_1 ^α (1/(t^α ((√(t^2 −1)))))dt, in function of real α. Calculate I(α) for α=1;2;4.

$${study}\:{the}\:{convergence}\:{of}: \\ $$$${I}\left(\alpha\right)=\int_{\mathrm{1}} ^{\alpha} \frac{\mathrm{1}}{{t}^{\alpha} \left(\sqrt{{t}^{\mathrm{2}} −\mathrm{1}}\right)}{dt},\:{in}\:{function}\: \\ $$$${of}\:{real}\:\alpha. \\ $$$${Calculate}\:{I}\left(\alpha\right)\:{for}\:\alpha=\mathrm{1};\mathrm{2};\mathrm{4}.\: \\ $$

Question Number 172287 Answers: 0 Comments: 0

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