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AllQuestion and Answers: Page 1667

Question Number 40594 Answers: 1 Comments: 1

Question Number 40587 Answers: 0 Comments: 1

find ∫e^x lnx dx

$$\boldsymbol{\mathrm{find}}\:\int\boldsymbol{\mathrm{e}}^{\boldsymbol{{x}}} \boldsymbol{\mathrm{ln}{x}}\:\boldsymbol{\mathrm{d}{x}} \\ $$

Question Number 40583 Answers: 2 Comments: 0

2^(√x) = x find x

$$\mathrm{2}^{\sqrt{{x}}} =\:{x} \\ $$$${find}\:{x} \\ $$

Question Number 40581 Answers: 1 Comments: 2

Question Number 40580 Answers: 0 Comments: 3

find ∫_0 ^∞ ((ln(1+ix))/(x^3 +8))dx

$${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left(\mathrm{1}+{ix}\right)}{{x}^{\mathrm{3}} \:+\mathrm{8}}{dx} \\ $$$$ \\ $$

Question Number 40591 Answers: 1 Comments: 1

Question Number 40569 Answers: 0 Comments: 0

Question Number 40551 Answers: 1 Comments: 5

Question Number 40550 Answers: 1 Comments: 0

if three numbers are drawn at random successively without replacement from a set S={1,2,......10}then probability that the minimum of the choosen number is 3 or their maximum is 7 Answer=((11)/(40))

$$\mathrm{if}\:\mathrm{three}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{drawn}\:\mathrm{at}\:\mathrm{random} \\ $$$$\mathrm{successively}\:\mathrm{without}\:\mathrm{replacement}\:\mathrm{from} \\ $$$$\mathrm{a}\:\mathrm{set}\:\mathrm{S}=\left\{\mathrm{1},\mathrm{2},......\mathrm{10}\right\}\mathrm{then}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{minimum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{choosen}\:\mathrm{number}\:\mathrm{is} \\ $$$$\mathrm{3}\:\mathrm{or}\:\mathrm{their}\:\mathrm{maximum}\:\mathrm{is}\:\mathrm{7}\:\:\:\:\:\:\:\: \\ $$$$\:\mathrm{Answer}=\frac{\mathrm{11}}{\mathrm{40}} \\ $$

Question Number 40523 Answers: 1 Comments: 1

If (1+ax+bx^2 )(1−2x)^(18) can be expanded using binomial theorem in ascending power of x.Determine the value of a and b,if the coefficient of x^3 and x^(4 ) are both zero.

$${If}\:\left(\mathrm{1}+{ax}+{bx}^{\mathrm{2}} \right)\left(\mathrm{1}−\mathrm{2}{x}\right)^{\mathrm{18}} \:\:{can}\:{be}\:{expanded}\:{using} \\ $$$${binomial}\:{theorem}\:{in}\:{ascending}\:{power}\:{of}\:{x}.{Determine} \\ $$$${the}\:{value}\:{of}\:\:\:{a}\:{and}\:{b},{if}\:{the}\:{coefficient}\:{of}\:{x}^{\mathrm{3}} \:\:{and}\:{x}^{\mathrm{4}\:} \:\:{are}\:{both}\:{zero}. \\ $$

Question Number 40544 Answers: 1 Comments: 0

solve for x 3^((2x−1)) −4(3^x )+1=0

$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{{x}} \\ $$$$\mathrm{3}^{\left(\mathrm{2}\boldsymbol{{x}}−\mathrm{1}\right)} −\mathrm{4}\left(\mathrm{3}^{\boldsymbol{{x}}} \right)+\mathrm{1}=\mathrm{0} \\ $$

Question Number 40519 Answers: 1 Comments: 1

Question Number 40499 Answers: 1 Comments: 0

A particle of mass 2×10^(−27) kg moves according to the following y=5cos(((πt)/3)+(π/4)) find the maximum kinetic energy

$${A}\:{particle}\:{of}\:{mass}\:\mathrm{2}×\mathrm{10}^{−\mathrm{27}} {kg}\:{moves} \\ $$$${according}\:{to}\:{the}\:{following} \\ $$$${y}=\mathrm{5}{cos}\left(\frac{\pi{t}}{\mathrm{3}}+\frac{\pi}{\mathrm{4}}\right) \\ $$$${find}\:{the}\:{maximum}\:{kinetic}\:{energy} \\ $$

Question Number 40498 Answers: 1 Comments: 0

A gas at 17° has the ratio of its initial to final volume as 25 with initial pressure of 2×10^5 Nm^(−2) .Calculate the final pressure and temperature after compression.(γ=1.5)

$${A}\:{gas}\:{at}\:\mathrm{17}°\:{has}\:{the}\:{ratio}\:{of}\:{its}\:{initial} \\ $$$${to}\:{final}\:{volume}\:{as}\:\mathrm{25}\:{with}\:{initial} \\ $$$${pressure}\:{of}\:\mathrm{2}×\mathrm{10}^{\mathrm{5}} {Nm}^{−\mathrm{2}} .{Calculate} \\ $$$${the}\:{final}\:{pressure}\:{and}\:{temperature} \\ $$$${after}\:{compression}.\left(\gamma=\mathrm{1}.\mathrm{5}\right) \\ $$

Question Number 40497 Answers: 0 Comments: 1

please i want to have applications of limits in maths and other sciences

$${please}\:{i}\:{want}\:{to}\:{have}\:{applications}\:{of}\: \\ $$$${limits}\:{in}\:{maths}\:{and}\:{other}\:{sciences}\: \\ $$$$ \\ $$

Question Number 40505 Answers: 1 Comments: 0

calcilate ∫_(π/6) ^(π/4) ((sin(x))/(cos(x) +cos(2x)))dx

$${calcilate}\:\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\frac{{sin}\left({x}\right)}{{cos}\left({x}\right)\:+{cos}\left(\mathrm{2}{x}\right)}{dx} \\ $$

Question Number 40504 Answers: 1 Comments: 0

let u_n =Σ_(k=1) ^n (1/(n^2 +k)) find lim_(n→+∞) n{1−n u_n } .

$${let}\:{u}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} +{k}} \\ $$$${find}\:{lim}_{{n}\rightarrow+\infty} {n}\left\{\mathrm{1}−{n}\:{u}_{{n}} \right\}\:. \\ $$

Question Number 40510 Answers: 1 Comments: 0

Given that ax+b is a factor of x^2 +2x^2 −1 and −a is a root of x^2 +2x −1=0 show that the value of b is −1 or 3+2(√(2 .))