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Question Number 38106    Answers: 0   Comments: 1

calculate ∫_0 ^(+∞) e^(−3t) ln(1+e^t )dt .

$${calculate}\:\:\int_{\mathrm{0}} ^{+\infty} \:\:{e}^{−\mathrm{3}{t}} {ln}\left(\mathrm{1}+{e}^{{t}} \right){dt}\:. \\ $$

Question Number 38105    Answers: 1   Comments: 0

find ∫ (dx/((√(2x+1)) +(√(2x−1))))

$${find}\:\int\:\:\:\:\:\frac{{dx}}{\sqrt{\mathrm{2}{x}+\mathrm{1}}\:+\sqrt{\mathrm{2}{x}−\mathrm{1}}}\: \\ $$

Question Number 38104    Answers: 1   Comments: 0

find ∫_1 ^(+∞) (dx/((x^2 +2)(√(x+3))))

$${find}\:\:\int_{\mathrm{1}} ^{+\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{2}\right)\sqrt{{x}+\mathrm{3}}} \\ $$

Question Number 38103    Answers: 0   Comments: 0

find I(λ)= ∫_0 ^(π/2) ((xdx)/(λ +tanx)) λ from R.

$${find}\:{I}\left(\lambda\right)=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\frac{{xdx}}{\lambda\:+{tanx}}\:\:\lambda\:{from}\:{R}. \\ $$

Question Number 38102    Answers: 0   Comments: 0

let B_n = ∫_0 ^n e^(−(x−[x])^2 ) dx 1) calculate B_n 2) find lim_(n→+∞) B_n

$${let}\:{B}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \:{e}^{−\left({x}−\left[{x}\right]\right)^{\mathrm{2}} } {dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{B}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{B}_{{n}} \\ $$

Question Number 38101    Answers: 0   Comments: 1

let A_n = ∫_0 ^n e^(x−[x]) dx 1) calculate A_n 2) find lim_(n→+∞) A_n

$${let}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \:\:{e}^{{x}−\left[{x}\right]} {dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$

Question Number 38100    Answers: 0   Comments: 1

let A_n = ∫_0 ^n (x−[x])^2 dx 1) calculate A_n 2) find lim_(n→+∞) A_n

$${let}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \left({x}−\left[{x}\right]\right)^{\mathrm{2}} {dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$

Question Number 38099    Answers: 0   Comments: 5

x^x =0.25 find x

$${x}^{{x}} =\mathrm{0}.\mathrm{25} \\ $$$${find}\:{x} \\ $$

Question Number 38094    Answers: 1   Comments: 12

Question Number 38092    Answers: 0   Comments: 5

Question Number 38079    Answers: 1   Comments: 4

Question Number 38074    Answers: 1   Comments: 4

∫(dx/(a+btan^2 x)) = ?

$$\int\frac{{dx}}{{a}+{b}\mathrm{tan}\:^{\mathrm{2}} {x}}\:=\:? \\ $$

Question Number 38062    Answers: 0   Comments: 3

Question Number 38059    Answers: 1   Comments: 0

Prove that Σ(x_i −x^− )=0

$${Prove}\:{that}\:\Sigma\left({x}_{{i}} −\overset{−} {{x}}\right)=\mathrm{0} \\ $$

Question Number 38058    Answers: 3   Comments: 0

∫((tan x)/(a+btan^2 x)) dx = ?

$$\int\frac{\mathrm{tan}\:{x}}{{a}+{b}\mathrm{tan}\:^{\mathrm{2}} {x}}\:{dx}\:\:=\:? \\ $$

Question Number 38057    Answers: 1   Comments: 0

∫((cos 5x+cos 4x)/(1−2cos 3x))dx = ?

$$\int\frac{\mathrm{cos}\:\mathrm{5}{x}+\mathrm{cos}\:\mathrm{4}{x}}{\mathrm{1}−\mathrm{2cos}\:\mathrm{3}{x}}{dx}\:\:=\:? \\ $$

Question Number 38051    Answers: 0   Comments: 0

A manufactual plans to build two types of tables. For table A,the cost of material is 20 000 bucks, the number of man hours needed to complete it is 10, and the profit is 15 000 bucks. Table B requires materials costing 12000 bucks,15 man hour of labour and makes same profit as table A. The total money avialable for materials is 500 000 bucks and labour avialable is 330 man hours.Find the maximum profit that can be made and the number of each type of table that should be made to produces it.

$${A}\:{manufactual}\:{plans}\:{to}\:{build}\:{two} \\ $$$${types}\:{of}\:{tables}.\:{For}\:{table}\:{A},{the}\:{cost} \\ $$$${of}\:{material}\:{is}\:\mathrm{20}\:\mathrm{000}\:{bucks},\:{the}\: \\ $$$${number}\:{of}\:{man}\:{hours}\:{needed}\:{to}\: \\ $$$${complete}\:{it}\:{is}\:\mathrm{10},\:{and}\:{the}\:{profit}\: \\ $$$${is}\:\mathrm{15}\:\mathrm{000}\:{bucks}.\:{Table}\:{B}\:{requires} \\ $$$${materials}\:{costing}\:\mathrm{12000}\:{bucks},\mathrm{15} \\ $$$${man}\:{hour}\:{of}\:{labour}\:{and}\:{makes} \\ $$$${same}\:{profit}\:{as}\:{table}\:{A}. \\ $$$$\:\:{The}\:{total}\:{money}\:{avialable}\:{for}\:{materials} \\ $$$${is}\:\mathrm{500}\:\mathrm{000}\:{bucks}\:{and}\:{labour}\:{avialable} \\ $$$${is}\:\mathrm{330}\:{man}\:{hours}.{Find}\:{the}\:{maximum} \\ $$$${profit}\:{that}\:{can}\:{be}\:{made}\:{and}\:{the}\:{number}\:{of}\:{each} \\ $$$${type}\:{of}\:{table}\:{that}\:{should}\:{be}\:{made}\:{to}\:{produces} \\ $$$${it}. \\ $$

Question Number 38049    Answers: 1   Comments: 0

Find the equation of the two lines throught (2,−3) which makes 45° with the line 2x − y = 2..hence find the cosine of the acute between the lines l_1 : y− 2x + 5=0 and l_2 : y − x + 6 (leave your answer in surd form)

$${Find}\:{the}\:{equation}\:{of}\:{the}\:{two}\:{lines} \\ $$$${throught}\:\left(\mathrm{2},−\mathrm{3}\right)\:{which}\:{makes}\:\mathrm{45}° \\ $$$${with}\:{the}\:{line}\:\mathrm{2}{x}\:−\:{y}\:=\:\mathrm{2}..{hence} \\ $$$${find}\:{the}\:{cosine}\:{of}\:{the}\:{acute}\:{between} \\ $$$${the}\:{lines}\:{l}_{\mathrm{1}} :\:{y}−\:\mathrm{2}{x}\:+\:\mathrm{5}=\mathrm{0}\:{and}\: \\ $$$${l}_{\mathrm{2}} :\:{y}\:−\:{x}\:+\:\mathrm{6}\:\left({leave}\:{your}\:{answer}\:{in}\right. \\ $$$$\left.{surd}\:{form}\right) \\ $$

Question Number 38044    Answers: 2   Comments: 1

Question Number 38032    Answers: 1   Comments: 1

Question Number 38025    Answers: 1   Comments: 0

An AP has 41 terms.The sum of the first five terms of this AP is 35 and the sum of the last five terms of the same AP is 395. find the common difference and the first term.

$$\boldsymbol{\mathrm{An}}\:\boldsymbol{\mathrm{AP}}\:\boldsymbol{\mathrm{has}}\:\mathrm{41}\:\boldsymbol{\mathrm{terms}}.\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{first}}\:\boldsymbol{\mathrm{five}} \\ $$$$\boldsymbol{\mathrm{terms}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{AP}}\:\boldsymbol{\mathrm{is}}\:\mathrm{35}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{sum}} \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{last}}\:\boldsymbol{\mathrm{five}}\:\boldsymbol{\mathrm{terms}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{same}}\:\boldsymbol{\mathrm{AP}}\:\boldsymbol{\mathrm{is}}\:\mathrm{395}. \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{common}}\:\boldsymbol{\mathrm{difference}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{first}}\:\boldsymbol{\mathrm{term}}. \\ $$

Question Number 38024    Answers: 1   Comments: 0

Question Number 38015    Answers: 0   Comments: 6

Question Number 38012    Answers: 3   Comments: 1

The roots of the equation 2x^2 − x + 3 = 0 are α and β if the roots of 3x^2 + px + q=0 are α + (1/α) and β + (1/(β )) find the value of p and q.

$${The}\:{roots}\:{of}\:{the}\:{equation} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} \:−\:{x}\:+\:\mathrm{3}\:=\:\mathrm{0}\:{are}\:\alpha\:{and}\:\beta \\ $$$${if}\:{the}\:{roots}\:{of}\:\mathrm{3}{x}^{\mathrm{2}} \:+\:{px}\:+\:{q}=\mathrm{0}\: \\ $$$${are}\:\alpha\:+\:\frac{\mathrm{1}}{\alpha}\:{and}\:\beta\:+\:\frac{\mathrm{1}}{\beta\:}\:{find}\:{the}\:{value} \\ $$$${of}\:{p}\:{and}\:{q}. \\ $$$$\: \\ $$

Question Number 38011    Answers: 2   Comments: 0

Show that ((sin2A)/(1+ cos2A)) = TanA

$${Show}\:{that}\: \\ $$$$\:\:\frac{{sin}\mathrm{2}{A}}{\mathrm{1}+\:{cos}\mathrm{2}{A}}\:=\:{TanA} \\ $$

Question Number 38006    Answers: 1   Comments: 5

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