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Question Number 69572 Answers: 1 Comments: 0

Question Number 69571 Answers: 1 Comments: 0

Question Number 69570 Answers: 0 Comments: 0

Question Number 69569 Answers: 2 Comments: 0

Question Number 69568 Answers: 1 Comments: 3

Question Number 69567 Answers: 0 Comments: 2

Question Number 69566 Answers: 1 Comments: 0

Question Number 69565 Answers: 0 Comments: 0

Question Number 69564 Answers: 0 Comments: 3

let f(a) =∫_0 ^∞ (dx/(x^4 −2x^2 +a)) with a real and a>1 1) determine a explicit form for f(a) 2) calculate g(a) =∫_0 ^∞ (dx/((x^4 −2x^2 +a)^2 )) 3) find the values of integrals ∫_0 ^∞ (dx/(x^4 −2x^2 +3)) and ∫_0 ^∞ (dx/((x^4 −2x^2 +3)^2 ))

$${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} \:+{a}}\:\:\:{with}\:{a}\:{real}\:{and}\:{a}>\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:\:{calculate}\:{g}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} +{a}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{values}\:{of}\:{integrals}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} \:+\mathrm{3}} \\ $$$${and}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$ \\ $$

Question Number 69563 Answers: 0 Comments: 1

calculate ∫_0 ^∞ (dx/(x^4 −x^2 +1))

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} \:+\mathrm{1}} \\ $$

Question Number 69610 Answers: 0 Comments: 0

Question Number 69609 Answers: 0 Comments: 2

Question Number 69608 Answers: 1 Comments: 2

Question Number 69607 Answers: 0 Comments: 4

without using lhospital please prove that lim_(x→0) ((x−sin x)/x^3 ) = (1/6) I want every method possible because someone challenge me

$$\boldsymbol{{without}}\:\boldsymbol{{using}}\:\boldsymbol{{lhospital}}\:\boldsymbol{{please}} \\ $$$$\boldsymbol{{prove}}\:\boldsymbol{{that}} \\ $$$$\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{lim}}}\:\frac{\boldsymbol{{x}}−\boldsymbol{{sin}}\:\boldsymbol{{x}}}{\boldsymbol{{x}}^{\mathrm{3}} }\:=\:\frac{\mathrm{1}}{\mathrm{6}} \\ $$$$\boldsymbol{{I}}\:\boldsymbol{{want}}\:\boldsymbol{{every}}\:\boldsymbol{{method}} \\ $$$$\boldsymbol{{possible}}\:\boldsymbol{{because}}\:\boldsymbol{{someone}} \\ $$$$\boldsymbol{{challenge}}\:\boldsymbol{{me}}\: \\ $$

Question Number 69557 Answers: 1 Comments: 0

Question Number 69620 Answers: 0 Comments: 1

Question Number 69545 Answers: 0 Comments: 2

Question Number 69538 Answers: 0 Comments: 0

Hello Verry Nice Day for You Find Σ_(k≥0) (1/((8k+1)^2 ))

$${Hello}\:{Verry}\:{Nice}\:{Day}\:{for}\:\:{You} \\ $$$${Find}\:\underset{{k}\geqslant\mathrm{0}} {\sum}\frac{\mathrm{1}}{\left(\mathrm{8}{k}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 69535 Answers: 3 Comments: 1

Question Number 69586 Answers: 0 Comments: 0

x^5 −x^4 −x^3 −x^2 −x−1=0

$${x}^{\mathrm{5}} −{x}^{\mathrm{4}} −{x}^{\mathrm{3}} −{x}^{\mathrm{2}} −{x}−\mathrm{1}=\mathrm{0} \\ $$

Question Number 69502 Answers: 3 Comments: 2

∫((3sinx+4cosx)/(4sinx+3cosx))dx

$$\int\frac{\mathrm{3sinx}+\mathrm{4cosx}}{\mathrm{4sinx}+\mathrm{3cosx}}\mathrm{dx} \\ $$

Question Number 69500 Answers: 2 Comments: 0

Question Number 69496 Answers: 0 Comments: 5

Question Number 69494 Answers: 1 Comments: 3

Question Number 69493 Answers: 0 Comments: 0

Question Number 69589 Answers: 0 Comments: 0

x^3 +px−ry+qz+a=0 y^3 +rx+qy−pz+b=0 z^3 −qx+py+rz+c=0 solve for x,y,z, in terms of p,q,r, a,b,c.

$${x}^{\mathrm{3}} +{px}−{ry}+{qz}+{a}=\mathrm{0} \\ $$$${y}^{\mathrm{3}} +{rx}+{qy}−{pz}+{b}=\mathrm{0} \\ $$$${z}^{\mathrm{3}} −{qx}+{py}+{rz}+{c}=\mathrm{0} \\ $$$${solve}\:{for}\:{x},{y},{z},\:{in}\:{terms}\:{of} \\ $$$${p},{q},{r},\:{a},{b},{c}. \\ $$

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