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Question Number 38115    Answers: 0   Comments: 0

find ∫_0 ^∞ ((sin(2x))/(sh(3x)))dx

$${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{{sh}\left(\mathrm{3}{x}\right)}{dx}\: \\ $$

Question Number 38114    Answers: 0   Comments: 2

let I_n = ∫_0 ^(2π) (dx/((p +cost)^n )) with p>1 find the value of I_n

$${let}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\:\frac{{dx}}{\left({p}\:+{cost}\right)^{{n}} }\:\:{with}\:{p}>\mathrm{1} \\ $$$${find}\:{the}\:{value}\:{of}\:{I}_{{n}} \\ $$

Question Number 38113    Answers: 0   Comments: 2

let p>1 calculate ∫_0 ^(2π) (dt/((p +cost)^2 ))

$${let}\:{p}>\mathrm{1}\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\:\:\:\frac{{dt}}{\left({p}\:+{cost}\right)^{\mathrm{2}} } \\ $$

Question Number 38112    Answers: 1   Comments: 1

prove that arctan(x)= (i/2)ln(((i+x)/(i−x))) for ∣x∣<1

$${prove}\:{that}\:\:{arctan}\left({x}\right)=\:\frac{{i}}{\mathrm{2}}{ln}\left(\frac{{i}+{x}}{{i}−{x}}\right)\:{for}\:\mid{x}\mid<\mathrm{1} \\ $$

Question Number 38111    Answers: 1   Comments: 1

find lim_(x→0) ((e^x −[x])/x)

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\frac{{e}^{{x}} \:−\left[{x}\right]}{{x}} \\ $$

Question Number 38110    Answers: 0   Comments: 0

let x from R find the value of f(x)= ∫_0 ^π ln(x^2 −2x cosθ +1)dθ

$${let}\:{x}\:{from}\:{R}\:{find}\:{the}\:{value}\:{of} \\ $$$${f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\pi} {ln}\left({x}^{\mathrm{2}} \:−\mathrm{2}{x}\:{cos}\theta\:+\mathrm{1}\right){d}\theta \\ $$

Question Number 38109    Answers: 0   Comments: 2

1) find S(x) = Σ_(n=1) ^∞ ((cos(nx))/n) 2) find Σ_(n=1) ^∞ (((−1)^n )/n)

$$\left.\mathrm{1}\right)\:{find}\:\:{S}\left({x}\right)\:=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{cos}\left({nx}\right)}{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}} \\ $$$$ \\ $$

Question Number 38108    Answers: 0   Comments: 1

find Σ_(n=1) ^∞ (((−1)^n )/n^2 )

$${find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} } \\ $$

Question Number 38107    Answers: 0   Comments: 0

find C = Σ_(n=1) ^∞ ((cos(nx))/n^2 )dx and S=Σ_(n=1) ^∞ ((sin(nx))/n^2 )

$${find}\:{C}\:=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{{cos}\left({nx}\right)}{{n}^{\mathrm{2}} }{dx}\:\:{and}\:{S}=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{sin}\left({nx}\right)}{{n}^{\mathrm{2}} } \\ $$

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.

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

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