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Question Number 70949 Answers: 1 Comments: 3

Question Number 70920 Answers: 1 Comments: 2

i ! = ?

$$\mathrm{i}\:!\:\:=\:\:? \\ $$

Question Number 70915 Answers: 1 Comments: 1

Question Number 70914 Answers: 2 Comments: 3

1+(z+2i)+(z+2i)^2 +(z+2i)^3 +(z+2i)^4 =0 find z , z∈C

$$\mathrm{1}+\left(\mathrm{z}+\mathrm{2i}\right)+\left(\mathrm{z}+\mathrm{2i}\right)^{\mathrm{2}} +\left(\mathrm{z}+\mathrm{2i}\right)^{\mathrm{3}} +\left(\mathrm{z}+\mathrm{2i}\right)^{\mathrm{4}} =\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{z}\:,\:\mathrm{z}\in\mathrm{C} \\ $$

Question Number 70917 Answers: 1 Comments: 3

∫(√(tan^2 x+3)) dx

$$\int\sqrt{{tan}^{\mathrm{2}} {x}+\mathrm{3}}\:{dx} \\ $$

Question Number 70909 Answers: 1 Comments: 2

Question Number 70913 Answers: 1 Comments: 4

Question Number 70898 Answers: 2 Comments: 0

Solve : 1.) (√(x−2)) + (√(4−x)) = x^2 −6x+11 2.) x^4 + x^3 − 2ax^2 − ax + a^2 = 0

$$\boldsymbol{{Solve}}\::\: \\ $$$$\left.\mathrm{1}.\right)\:\:\sqrt{\boldsymbol{{x}}−\mathrm{2}}\:+\:\sqrt{\mathrm{4}−\boldsymbol{{x}}}\:=\:\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{6}\boldsymbol{{x}}+\mathrm{11} \\ $$$$\left.\mathrm{2}.\right)\:\:\boldsymbol{{x}}^{\mathrm{4}} \:+\:\boldsymbol{{x}}^{\mathrm{3}} \:−\:\mathrm{2}\boldsymbol{{ax}}^{\mathrm{2}} \:−\:\boldsymbol{{ax}}\:+\:\boldsymbol{{a}}^{\mathrm{2}} \:=\:\mathrm{0} \\ $$

Question Number 70891 Answers: 0 Comments: 2

f(x) = x(x−1)(x−2)....(x−10) f ′(0) = ?

$$\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\:=\:\boldsymbol{{x}}\left(\boldsymbol{{x}}−\mathrm{1}\right)\left(\boldsymbol{{x}}−\mathrm{2}\right)....\left(\boldsymbol{{x}}−\mathrm{10}\right) \\ $$$$\boldsymbol{{f}}\:'\left(\mathrm{0}\right)\:=\:? \\ $$

Question Number 70885 Answers: 1 Comments: 0

(2)^(1/3) = a + (1/(b + (1/(c + (1/(d + …)))))) a, b, c, d ∈ Z^+ What′s b ?

$$\sqrt[{\mathrm{3}}]{\mathrm{2}}\:\:=\:{a}\:+\:\frac{\mathrm{1}}{{b}\:+\:\frac{\mathrm{1}}{{c}\:+\:\frac{\mathrm{1}}{{d}\:+\:\ldots}}} \\ $$$${a},\:{b},\:{c},\:{d}\:\:\in\:\mathbb{Z}^{+} \\ $$$${What}'{s}\:\:{b}\:\:? \\ $$

Question Number 70876 Answers: 0 Comments: 0

Prove that The necessary and sufficient condition that the curve be plane (curve) is [r′,r′′,r′′′]=0. OR A curve is plane curve iff τ=0.

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{The}\:\mathrm{necessary}\:\mathrm{and}\:\mathrm{sufficient}\:\mathrm{condition} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{be}\:\mathrm{plane}\:\left(\mathrm{curve}\right)\:\mathrm{is} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\left[\boldsymbol{\mathrm{r}}',\boldsymbol{\mathrm{r}}'',\boldsymbol{\mathrm{r}}'''\right]=\mathrm{0}. \\ $$$$\:\mathrm{OR}\:\:\:\: \\ $$$$\mathrm{A}\:\mathrm{curve}\:\mathrm{is}\:\mathrm{plane}\:\mathrm{curve}\:\mathrm{iff}\:\tau=\mathrm{0}. \\ $$

Question Number 70874 Answers: 2 Comments: 0

If 4−2(√5) and 4+2(√(5 )) are solutions of x^2 +(5a−b)x+(3b−a)=0 whete a and b are real numbers, determine the product of ab.

$${If}\:\mathrm{4}−\mathrm{2}\sqrt{\mathrm{5}}\:{and}\:\mathrm{4}+\mathrm{2}\sqrt{\mathrm{5}\:}\:{are}\:{solutions} \\ $$$${of}\:{x}^{\mathrm{2}} +\left(\mathrm{5}{a}−{b}\right){x}+\left(\mathrm{3}{b}−{a}\right)=\mathrm{0} \\ $$$${whete}\:{a}\:{and}\:{b}\:{are}\:{real}\:{numbers},\: \\ $$$${determine}\:{the}\:{product}\:{of}\:\boldsymbol{{ab}}. \\ $$

Question Number 70873 Answers: 1 Comments: 0

calculate ∫∫_([1,3]^2 ) e^(−x−y) ln(2x+y)dxdy

$${calculate}\:\int\int_{\left[\mathrm{1},\mathrm{3}\right]^{\mathrm{2}} } \:\:\:{e}^{−{x}−{y}} \:{ln}\left(\mathrm{2}{x}+{y}\right){dxdy} \\ $$

Question Number 70872 Answers: 0 Comments: 1

calculate ∫∫_([1,3]^2 ) e^(−x−y) ln(2x+y)dxdy

$${calculate}\:\int\int_{\left[\mathrm{1},\mathrm{3}\right]^{\mathrm{2}} } \:\:\:{e}^{−{x}−{y}} \:{ln}\left(\mathrm{2}{x}+{y}\right){dxdy} \\ $$

Question Number 70871 Answers: 0 Comments: 1

calculate f(x)=∫_(−∞) ^(+∞) ((cos(x(1+t^2 )))/(1+t^2 ))dt with x≥0

$$\:{calculate}\:{f}\left({x}\right)=\int_{−\infty} ^{+\infty} \:\frac{{cos}\left({x}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)\right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:{with}\:{x}\geqslant\mathrm{0} \\ $$

Question Number 70887 Answers: 0 Comments: 2

Question Number 70865 Answers: 0 Comments: 2

Question Number 70870 Answers: 0 Comments: 4

let f(x)=∫_(−∞) ^(+∞) (dt/((t^2 −2t +x^2 )^4 )) with ∣x∣>1 and n integr natural 1)find a explicit form for f(x) 2) determine also g(x)=∫_(−∞) ^(+∞) (dt/((t^2 −2t +x^2 )^5 )) 3)find the values of integrals ∫_(−∞) ^(+∞) (dt/((t^2 −2t +3)^4 )) and ∫_(−∞) ^(+∞) (dt/((t^2 −2t +3)^5 ))

$${let}\:{f}\left({x}\right)=\int_{−\infty} ^{+\infty} \:\:\frac{{dt}}{\left({t}^{\mathrm{2}} −\mathrm{2}{t}\:+{x}^{\mathrm{2}} \right)^{\mathrm{4}} }\:\:{with}\:\:\mid{x}\mid>\mathrm{1} \\ $$$${and}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right){find}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{also}\:{g}\left({x}\right)=\int_{−\infty} ^{+\infty} \:\:\frac{{dt}}{\left({t}^{\mathrm{2}} −\mathrm{2}{t}\:+{x}^{\mathrm{2}} \right)^{\mathrm{5}} } \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{values}\:{of}\:{integrals}\: \\ $$$$\int_{−\infty} ^{+\infty} \:\frac{{dt}}{\left({t}^{\mathrm{2}} −\mathrm{2}{t}\:+\mathrm{3}\right)^{\mathrm{4}} }\:\:{and}\:\int_{−\infty} ^{+\infty} \:\frac{{dt}}{\left({t}^{\mathrm{2}} −\mathrm{2}{t}\:+\mathrm{3}\right)^{\mathrm{5}} } \\ $$

Question Number 70886 Answers: 2 Comments: 11