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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.

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

Question Number 37972 Answers: 1 Comments: 0

The distance S metres is given as a funtion f(t) where is time taken... if S = t^3 + t^2 + 4 find the velocity and acceleration

$$\:{The}\:{distance}\:{S}\:{metres}\:{is}\: \\ $$$${given}\:{as}\:{a}\:{funtion}\: \\ $$$${f}\left({t}\right)\:{where}\:{is}\:{time}\:{taken}... \\ $$$${if}\:{S}\:=\:{t}^{\mathrm{3}} \:+\:{t}^{\mathrm{2}} \:+\:\mathrm{4} \\ $$$${find}\:{the}\:{velocity}\:{and}\:{acceleration} \\ $$

Question Number 37991 Answers: 1 Comments: 4

1. Find the sum s_n =1+2x+3x^2 +4x^3 +...+nx^(n−1) Hence,or otherwise, find the sum Σ_(k=1) ^n k.2^k 2. Simplify the following i. Σ_(r=0) ^n (_(2r−1) ^(2n) ) ii.Σ_(r=0) ^n (−1)^r r(_r ^n ) iii.Σ_(r=0) ^n (−1)^r (1/(r+1))(_r ^n ) iv.Σ_(r=0) ^n (_(2r) ^(2n) ) v.Σ_(r=0) ^n (−1)^r (_(n−r) ^(n+1) ) 3.Find the sum Σ_(r=0) ^(n−k) (_k ^(n−r) ), where k=0,1,2,3,...,n

$$\mathrm{1}.\:{Find}\:{the}\:{sum} \\ $$$$\:\:\:\:{s}_{{n}} =\mathrm{1}+\mathrm{2}{x}+\mathrm{3}{x}^{\mathrm{2}} +\mathrm{4}{x}^{\mathrm{3}} +...+{nx}^{{n}−\mathrm{1}} \\ $$$${Hence},{or}\:{otherwise},\:{find}\:{the}\:{sum} \\ $$$$\:\:\:\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}.\mathrm{2}^{{k}} \\ $$$$\mathrm{2}.\:{Simplify}\:{the}\:{following} \\ $$$${i}.\:\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\left(_{\mathrm{2}{r}−\mathrm{1}} ^{\mathrm{2}{n}} \right) \\ $$$${ii}.\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{r}} {r}\left(_{{r}} ^{{n}} \right) \\ $$$${iii}.\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{r}} \frac{\mathrm{1}}{{r}+\mathrm{1}}\left(_{{r}} ^{{n}} \right) \\ $$$${iv}.\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\left(_{\mathrm{2}{r}} ^{\mathrm{2}{n}} \right) \\ $$$${v}.\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{r}} \left(_{{n}−{r}} ^{{n}+\mathrm{1}} \right) \\ $$$$\mathrm{3}.{Find}\:{the}\:{sum} \\ $$$$\:\:\:\:\:\:\:\:\:\underset{{r}=\mathrm{0}} {\overset{{n}−{k}} {\sum}}\left(_{{k}} ^{{n}−{r}} \right),\:\:\:{where}\:{k}=\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},...,{n} \\ $$

Question Number 37989 Answers: 2 Comments: 7

Question Number 37964 Answers: 1 Comments: 0

Question Number 37961 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (dx/(x^(2 ) +(√(1+x^2 )))) .

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{{x}^{\mathrm{2}\:} \:+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:. \\ $$

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