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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

Question Number 61952 Answers: 1 Comments: 1

Question Number 61948 Answers: 0 Comments: 0

The vectors a, b, c are equal in length and taken pairwise, they make equal angles. If a=i+j, b=j+k and c makes an obtuse angle with X−axis, then c=

Question Number 61938 Answers: 0 Comments: 0

Question Number 61937 Answers: 1 Comments: 5

find the value of Σ_(n = 0) ^∞ ((n^3 + 5)/(n!))

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\:\:\:\underset{\mathrm{n}\:=\:\mathrm{0}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{n}^{\mathrm{3}} \:+\:\mathrm{5}}{\mathrm{n}!} \\ $$

Question Number 61934 Answers: 1 Comments: 2

Answer: 0^0 =?

$$\mathrm{Answer}:\:\mathrm{0}^{\mathrm{0}} =? \\ $$

Question Number 61923 Answers: 1 Comments: 0

Find all solutions of x^3 − 12x + 8 = 0

$${Find}\:\:{all}\:\:{solutions}\:\:{of} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{x}^{\mathrm{3}} \:−\:\mathrm{12}{x}\:+\:\mathrm{8}\:=\:\:\mathrm{0} \\ $$

Question Number 61922 Answers: 1 Comments: 3

Find the value of: Σ_(n = 1) ^∞ ((n^2 + 1)/(n + 2)). (x^n /(n!))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}:\:\:\:\:\:\underset{\mathrm{n}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{n}^{\mathrm{2}} \:+\:\mathrm{1}}{\mathrm{n}\:+\:\mathrm{2}}.\:\frac{\mathrm{x}^{\mathrm{n}} }{\mathrm{n}!} \\ $$

Question Number 61921 Answers: 1 Comments: 1

let A =∫_(−∞) ^(+∞) ((x+1)/((x^2 +x+1)( x^2 −2i)))dx 1) calculate A 2) extract Re(A) and Im(A) and determine its values (i^2 =−1)

$${let}\:{A}\:=\int_{−\infty} ^{+\infty} \:\:\:\:\:\frac{{x}+\mathrm{1}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)\left(\:{x}^{\mathrm{2}} \:−\mathrm{2}{i}\right)}{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A} \\ $$$$\left.\mathrm{2}\right)\:{extract}\:{Re}\left({A}\right)\:{and}\:{Im}\left({A}\right)\:{and}\:{determine}\:{its}\:{values}\:\:\:\left({i}^{\mathrm{2}} =−\mathrm{1}\right) \\ $$

Question Number 61915 Answers: 1 Comments: 0

1+iw+(iw)^2 +(iw)^3 +.........(iw)^(989) =? ans= (2/(1−iw)) answer is correct. pls help .. how to do this? TIA

$$\mathrm{1}+{iw}+\left({iw}\right)^{\mathrm{2}} +\left({iw}\right)^{\mathrm{3}} +.........\left({iw}\right)^{\mathrm{989}} =? \\ $$$$ \\ $$$${ans}=\:\:\:\:\frac{\mathrm{2}}{\mathrm{1}−{iw}}\:\:\:\:\:\:{answer}\:{is}\:{correct}. \\ $$$${pls}\:{help}\:..\:{how}\:{to}\:{do}\:{this}? \\ $$$${TIA} \\ $$

Question Number 61912 Answers: 0 Comments: 1

Question Number 61907 Answers: 1 Comments: 1

Question Number 61986 Answers: 1 Comments: 0

Find the area bounded by y(x+2)=x^4 , x=0,y=0 and x=3

$${Find}\:{the}\:{area}\:{bounded}\:{by}\:{y}\left({x}+\mathrm{2}\right)={x}^{\mathrm{4}} , \\ $$$${x}=\mathrm{0},{y}=\mathrm{0}\:{and}\:{x}=\mathrm{3} \\ $$

Question Number 61902 Answers: 0 Comments: 3

Question Number 61895 Answers: 0 Comments: 3

let A = (((1 −1)),((0 1)) ) 1) calculate A^n 2) find e^A ,e^(−A) 3) determine e^(iA) then cosA and sinA .

$${let}\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:−\mathrm{1}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}^{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{e}^{{A}} \:\:,{e}^{−{A}} \\ $$$$\left.\mathrm{3}\right)\:{determine}\:{e}^{{iA}} \:\:\:{then}\:\:{cosA}\:\:{and}\:{sinA}\:. \\ $$

Question Number 61892 Answers: 0 Comments: 1

(1/4) of (2/5)

$$\frac{\mathrm{1}}{\mathrm{4}}\:\mathrm{of}\:\frac{\mathrm{2}}{\mathrm{5}} \\ $$

Question Number 61886 Answers: 1 Comments: 0

a+bi=((2+i)/(1−i)) find 2(a^2 +b^2 )

$${a}+{bi}=\frac{\mathrm{2}+{i}}{\mathrm{1}−{i}} \\ $$$${find}\: \\ $$$$\mathrm{2}\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right) \\ $$

Question Number 61885 Answers: 0 Comments: 0

let I =∫_(−∞) ^(+∞) (dx/((x+i)^n )) and J =∫_(−∞) ^(+∞) (dx/((x−i)^n )) 1) calculate I and J interms of n 2) find thevalue of integral A_n =∫_(−∞) ^(+∞) (( cos(narctan((1/x))))/((1+x^2 )^(n/2) ))dx

$${let}\:{I}\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{\left({x}+{i}\right)^{{n}} }\:\:{and}\:{J}\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{\left({x}−{i}\right)^{{n}} } \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}\:{and}\:{J}\:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{thevalue}\:{of}\:{integral} \\ $$$${A}_{{n}} \:\:=\int_{−\infty} ^{+\infty} \:\:\:\frac{\:{cos}\left({narctan}\left(\frac{\mathrm{1}}{{x}}\right)\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\frac{{n}}{\mathrm{2}}} }{dx}\:\:\:\: \\ $$$$ \\ $$

Question Number 61884 Answers: 0 Comments: 3

let f_n (a) =∫_(−∞) ^(+∞) ((cos(nx))/((x^2 +x +a)^2 ))dx with a≥1 1) find a explicit form of f_n (a) 2)study the convervenge of Σ f_n (a) 3) determine also g_n (a) = ∫_(−∞) ^(+∞) ((cos(nx))/((x^2 +x+a)^3 ))dx study the convergence of Σ gn(a)

$${let}\:{f}_{{n}} \left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\:\:\frac{{cos}\left({nx}\right)}{\left({x}^{\mathrm{2}} +{x}\:\:+{a}\right)^{\mathrm{2}} }{dx}\:\:\:\:{with}\:\:\:{a}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}_{{n}} \left({a}\right) \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{convervenge}\:{of}\:\Sigma\:{f}_{{n}} \left({a}\right) \\ $$$$\left.\mathrm{3}\right)\:{determine}\:{also}\:{g}_{{n}} \left({a}\right)\:=\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{cos}\left({nx}\right)}{\left({x}^{\mathrm{2}} \:+{x}+{a}\right)^{\mathrm{3}} }{dx} \\ $$$${study}\:{the}\:{convergence}\:{of}\:\Sigma\:{gn}\left({a}\right) \\ $$

Question Number 61874 Answers: 0 Comments: 1

∫((xln(x)−x)/(ln^3 (x))) dx

$$\int\frac{{xln}\left({x}\right)−{x}}{{ln}^{\mathrm{3}} \left({x}\right)}\:{dx} \\ $$

Question Number 61873 Answers: 1 Comments: 2

((30x^8 y^(12) ))^(1/3) /^4 (√(6x^2 y^9 z)) simplifh this question

$$\sqrt[{\mathrm{3}}]{\mathrm{30x}^{\mathrm{8}} \mathrm{y}^{\mathrm{12}} }/^{\mathrm{4}} \sqrt{\mathrm{6x}^{\mathrm{2}} \mathrm{y}^{\mathrm{9}} \mathrm{z}}\:\:\:\:\mathrm{simplifh}\:\mathrm{this}\:\mathrm{question} \\ $$

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