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Question Number 62022 Answers: 1 Comments: 0

Question Number 62019 Answers: 0 Comments: 1

Question Number 62016 Answers: 0 Comments: 1

the 2 and 3 term of GP is 24 and 12(x+1).If the sum of the first 3 terms is 76.Find the value of x

$${the}\:\mathrm{2}\:{and}\:\mathrm{3}\:{term}\:{of}\:{GP}\:\:{is}\:\mathrm{24} \\ $$$${and}\:\mathrm{12}\left({x}+\mathrm{1}\right).{If}\:{the}\:{sum}\:{of}\:{the}\: \\ $$$${first}\:\mathrm{3}\:{terms}\:{is}\:\mathrm{76}.{Find}\:{the}\:{value} \\ $$$${of}\:{x} \\ $$

Question Number 62014 Answers: 1 Comments: 0

Question Number 62010 Answers: 0 Comments: 0

if x^2 +y^2 +z^2 −2xyz=1 prove that (dx/(√(1−x^2 ))) + (dy/(√(1−y^2 ))) + (dz/(√(1−z^2 ))) = 0

$${if}\: \\ $$$$ \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} −\mathrm{2}{xyz}=\mathrm{1} \\ $$$${prove}\:{that} \\ $$$$ \\ $$$$\frac{{dx}}{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:+\:\frac{{dy}}{\sqrt{\mathrm{1}−{y}^{\mathrm{2}} }}\:+\:\frac{{dz}}{\sqrt{\mathrm{1}−{z}^{\mathrm{2}} }}\:=\:\mathrm{0} \\ $$

Question Number 62003 Answers: 0 Comments: 0

let ξ(x) =Σ_(n=1) ^∞ (1/n^x ) with x>1 prove that ξ(x) =Π_(p prime) (1/(1−p^(−x) ))

$${let}\:\xi\left({x}\right)\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{{x}} }\:\:\:{with}\:{x}>\mathrm{1}\:\:{prove}\:{that}\:\:\xi\left({x}\right)\:=\prod_{{p}\:{prime}} \:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}−{p}^{−{x}} } \\ $$

Question Number 62002 Answers: 0 Comments: 0

Question Number 62001 Answers: 0 Comments: 1

find ∫_0 ^(π/4) (x^2 /(1−cos(x)))dx

$${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\frac{{x}^{\mathrm{2}} }{\mathrm{1}−{cos}\left({x}\right)}{dx}\: \\ $$

Question Number 62000 Answers: 0 Comments: 0

calculate ∫_0 ^1 ln(1+x)ln^2 (1−x)dx

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{ln}\left(\mathrm{1}+{x}\right){ln}^{\mathrm{2}} \left(\mathrm{1}−{x}\right){dx} \\ $$

Question Number 61994 Answers: 1 Comments: 1

Question Number 61993 Answers: 1 Comments: 0

ultraviolet light of wavelength 300×10^(−9) m causes photon emissions from a surface The stopping potential is 6V.Find the work-function in electron-Volts

$${ultraviolet}\:{light}\:{of}\:{wavelength}\:\mathrm{300}×\mathrm{10}^{−\mathrm{9}} {m} \\ $$$${causes}\:{photon}\:{emissions}\:{from}\:{a}\:{surface} \\ $$$${The}\:{stopping}\:{potential}\:{is}\:\mathrm{6}{V}.{Find}\:{the} \\ $$$${work}-{function}\:{in}\:{electron}-{Volts} \\ $$

Question Number 62046 Answers: 0 Comments: 1

4×(3+2−3)

$$\mathrm{4}×\left(\mathrm{3}+\mathrm{2}−\mathrm{3}\right) \\ $$

Question Number 61981 Answers: 0 Comments: 1

let A_n =∫_0 ^1 e^(nx) arctan((2/(n^2 +1)))dx calculate lim_(n→∞) A_n

$${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{{nx}} \:{arctan}\left(\frac{\mathrm{2}}{{n}^{\mathrm{2}} \:+\mathrm{1}}\right){dx}\:\:\:{calculate}\:{lim}_{{n}\rightarrow\infty} \:{A}_{{n}} \\ $$

Question Number 61979 Answers: 0 Comments: 1

find ∫_0 ^1 ln(x)ln(1+x) dx

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}\right){ln}\left(\mathrm{1}+{x}\right)\:{dx} \\ $$

Question Number 61978 Answers: 0 Comments: 5

let f(x) =∫_0 ^1 ln(1−xt^3 )dt with ∣x∣<1 1) find a explicit form of f(x) 2)calculate ∫_0 ^1 ln(1−(1/(√2))t^3 )dt 3) calculate A(θ) =∫_0 ^1 ln(1−sinθ t^3 )dt with 0<θ<(π/2)

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{xt}^{\mathrm{3}} \right){dt}\:\:{with}\:\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}{t}^{\mathrm{3}} \right){dt} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{A}\left(\theta\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{sin}\theta\:{t}^{\mathrm{3}} \right){dt}\:\:{with}\:\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}} \\ $$

Question Number 61976 Answers: 0 Comments: 2

let A_n = ∫_(1/n) ^n ((arctan(x^2 +y^2 ))/(x^2 +y^2 )) dxdy 1) calculate A_n 2) find lim_(n→∞) A_n

$${let}\:{A}_{{n}} =\:\int_{\frac{\mathrm{1}}{{n}}} ^{{n}} \:\:\:\frac{{arctan}\left({x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:{dxdy}\:\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow\infty} \:{A}_{{n}} \\ $$

Question Number 61966 Answers: 2 Comments: 4

∫(1/(e^(2x) −e^(−2x) )) dx

$$\int\frac{\mathrm{1}}{{e}^{\mathrm{2}{x}} −{e}^{−\mathrm{2}{x}} }\:{dx} \\ $$

Question Number 61954 Answers: 0 Comments: 1