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Question Number 33232 Answers: 0 Comments: 1

find the value of ∫_(−∞) ^(+∞) ((x sin(2x))/((1+4x^2 )^2 )) dx .

$${find}\:{the}\:{value}\:{of}\:\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{x}\:{sin}\left(\mathrm{2}{x}\right)}{\left(\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx}\:. \\ $$

Question Number 33200 Answers: 1 Comments: 0

Solve 2^(3n+2) −7×2^(2n+2) −31×2^n −8=0, n∈R. I need some help with this

$$\mathrm{Solve}\:\mathrm{2}^{\mathrm{3n}+\mathrm{2}} \:−\mathrm{7}×\mathrm{2}^{\mathrm{2n}+\mathrm{2}} \:−\mathrm{31}×\mathrm{2}^{\mathrm{n}} \:−\mathrm{8}=\mathrm{0},\:\mathrm{n}\in\boldsymbol{\mathrm{R}}. \\ $$$$\mathrm{I}\:\mathrm{need}\:\mathrm{some}\:\mathrm{help}\:\mathrm{with}\:\mathrm{this} \\ $$

Question Number 33199 Answers: 0 Comments: 1

Question Number 33195 Answers: 0 Comments: 0

Question Number 33193 Answers: 1 Comments: 0

Q. If α is a root of the equation x^3 −3x−1=0, prove that the other roots are 2−α^2 and α^2 −α−2. Please help.

$$\mathrm{Q}.\:\:\mathrm{If}\:\alpha\:\mathrm{is}\:\mathrm{a}\:\mathrm{root}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}^{\mathrm{3}} −\mathrm{3}{x}−\mathrm{1}=\mathrm{0}, \\ $$$$\:\:\:\:\:\:\:\:\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{other}\:\mathrm{roots}\:\mathrm{are} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{2}−\alpha^{\mathrm{2}} \:\mathrm{and}\:\alpha^{\mathrm{2}} −\alpha−\mathrm{2}. \\ $$$$\:\:\:\:\:\:\:\:\mathrm{Please}\:\mathrm{help}. \\ $$

Question Number 33186 Answers: 1 Comments: 0

Find the exact value of sinθ if cosθ=(1/(57)) and θ is obtuse

$${Find}\:{the}\:{exact}\:{value}\:{of}\:{sin}\theta\:{if} \\ $$$${cos}\theta=\frac{\mathrm{1}}{\mathrm{57}}\:{and}\:\theta\:{is}\:{obtuse} \\ $$

Question Number 33185 Answers: 1 Comments: 0

find k if Σ_(n=1) ^∞ (2k)(2)^(n−1) =64 hence find k if kx^2 +3x +4=0 has real roots.

$${find}\:{k}\:{if} \\ $$$$\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\mathrm{2}{k}\right)\left(\mathrm{2}\right)^{{n}−\mathrm{1}} =\mathrm{64} \\ $$$${hence}\:{find}\:{k}\:{if}\:\:{kx}^{\mathrm{2}} +\mathrm{3}{x}\:+\mathrm{4}=\mathrm{0}\:{has} \\ $$$${real}\:{roots}. \\ $$

Question Number 33184 Answers: 0 Comments: 0

describe geometrically the matrice (((1 0)),((0 −1)) )

$${describe}\:{geometrically}\:{the}\:{matrice} \\ $$$$\:\:\:\:\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:−\mathrm{1}}\end{pmatrix} \\ $$

Question Number 33202 Answers: 0 Comments: 1

find the value of ∫_(−∞) ^(+∞) (dt/((1+t +t^2 )^2 )) .

$${find}\:{the}\:{value}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\frac{{dt}}{\left(\mathrm{1}+{t}\:+{t}^{\mathrm{2}} \right)^{\mathrm{2}} }\:. \\ $$

Question Number 33175 Answers: 0 Comments: 1

find ∫_0 ^1 (dt/((1+t^2 )^2 ))

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$

Question Number 33174 Answers: 0 Comments: 0

let (a,b)∈N^2 and p_n (x)= (x^n /(n!))(bx−a)^n give the taylor formula for p_(n ) at x=0 .

$${let}\:\left({a},{b}\right)\in{N}^{\mathrm{2}} \:{and}\:{p}_{{n}} \left({x}\right)=\:\frac{{x}^{{n}} }{{n}!}\left({bx}−{a}\right)^{{n}} \\ $$$${give}\:{the}\:{taylor}\:{formula}\:{for}\:{p}_{{n}\:} \:{at}\:{x}=\mathrm{0}\:. \\ $$

Question Number 33173 Answers: 0 Comments: 0

let give f(x)= (1/(1+x^3 )) developp f at integr serie.

$${let}\:\:{give}\:{f}\left({x}\right)=\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{3}} }\:{developp}\:{f}\:\:{at}\:{integr}\:{serie}. \\ $$$$ \\ $$

Question Number 33172 Answers: 0 Comments: 0

find ∫ (dx/(x +(√(x^2 −3x+2)))) .

$${find}\:\:\int\:\:\:\:\frac{{dx}}{{x}\:+\sqrt{{x}^{\mathrm{2}} \:−\mathrm{3}{x}+\mathrm{2}}}\:. \\ $$

Question Number 33171 Answers: 0 Comments: 0

let f(x)= (1/(1−e^t )) .calculate f^′ (x) interms of cht

$${let}\:{f}\left({x}\right)=\:\:\frac{\mathrm{1}}{\mathrm{1}−{e}^{{t}} }\:\:.{calculate}\:{f}^{'} \left({x}\right)\:{interms}\:{of}\:{cht} \\ $$

Question Number 33170 Answers: 0 Comments: 1

prove that ∫_0 ^∞ ((∣sinx∣)/x) dx is divergent.

$${prove}\:{that}\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mid{sinx}\mid}{{x}}\:{dx}\:{is}\:{divergent}. \\ $$

Question Number 33169 Answers: 1 Comments: 1

find the value of ∫_0 ^π (dx/(1+2 sin^2 x)) .

$${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{dx}}{\mathrm{1}+\mathrm{2}\:{sin}^{\mathrm{2}} {x}}\:\:. \\ $$

Question Number 33168 Answers: 0 Comments: 1

find lim_(n→∞) ∫_n ^(n+1) (((t+n)^(1/3) )/(√t)) dt .

$${find}\:{lim}_{{n}\rightarrow\infty} \:\:\:\int_{{n}} ^{{n}+\mathrm{1}} \:\:\:\frac{\left({t}+{n}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} }{\sqrt{{t}}}\:{dt}\:. \\ $$

Question Number 33167 Answers: 0 Comments: 1

f is a continue and positive function on [a,b] with a<b let m =max_(x∈[a,b]) f(x) prove that lim_(n→∞) ( (1/(b−a)) ∫_a ^b f^n (x)dx)^(1/n)

$${f}\:{is}\:{a}\:{continue}\:{and}\:{positive}\:{function}\:{on}\:\left[{a},{b}\right]\:{with}\:{a}<{b} \\ $$$${let}\:{m}\:={max}_{{x}\in\left[{a},{b}\right]} \:{f}\left({x}\right)\:{prove}\:{that} \\ $$$${lim}_{{n}\rightarrow\infty} \:\:\left(\:\frac{\mathrm{1}}{{b}−{a}}\:\int_{{a}} ^{{b}} \:{f}^{{n}} \left({x}\right){dx}\right)^{\frac{\mathrm{1}}{{n}}} \\ $$

Question Number 33166 Answers: 0 Comments: 0

find the value of ∫_0 ^1 (dx/(1+x^4 )) .

$${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{4}} }\:\:. \\ $$

Question Number 33159 Answers: 0 Comments: 0

if y= 3x^4 find the percentage increase in y if x increases at (5/2)% or 2(1/2)%^ use the Binomial Expansion method (that is find new y and new x and simplify)

$${if}\:{y}=\:\mathrm{3}{x}^{\mathrm{4}} \:{find}\:{the}\:{percentage}\:{increase}\:{in}\:{y} \\ $$$${if}\:{x}\:{increases}\:{at}\:\frac{\mathrm{5}}{\mathrm{2}}\%\:{or}\:\mathrm{2}\frac{\mathrm{1}}{\mathrm{2}}\overset{} {\%} \\ $$$${use}\:{the}\:{Binomial}\:{Expansion}\:{method} \\ $$$$\left({that}\:{is}\:{find}\:{new}\:{y}\:{and}\:{new}\:{x}\:{and}\:{simplify}\right) \\ $$

Question Number 33158 Answers: 0 Comments: 2

the matrice which comes from the transformation matrix (((cosθ −sinθ)),((sin θ cosθ)) ) at 90° is?

$${the}\:{matrice}\:{which}\:{comes}\:{from} \\ $$$${the}\:{transformation}\:{matrix}\: \\ $$$$\:\begin{pmatrix}{{cos}\theta\:\:\:\:\:\:\:\:\:−{sin}\theta}\\{{sin}\:\theta\:\:\:\:\:\:\:\:\:\:\:\:\:\:{cos}\theta}\end{pmatrix} \\ $$$${at}\:\mathrm{90}°\:{is}? \\ $$

Question Number 33157 Answers: 0 Comments: 1

find k if kloga= loga + log a^2 + log a^(3 ) + log a^4

$${find}\:{k}\:{if} \\ $$$${kloga}=\:{loga}\:+\:{log}\:{a}^{\mathrm{2}} +\:{log}\:{a}^{\mathrm{3}\:} +\:{log}\:{a}^{\mathrm{4}} \\ $$

Question Number 33155 Answers: 0 Comments: 4

Evaluate ∫_(−∞) ^∞ 3x^2 (x^3 + 1)^2 e^(−x^6 − 2x^3 ) dx

$$\mathrm{Evaluate} \\ $$$$\int_{−\infty} ^{\infty} \:\mathrm{3}{x}^{\mathrm{2}} \left({x}^{\mathrm{3}} \:+\:\mathrm{1}\right)^{\mathrm{2}} \:{e}^{−{x}^{\mathrm{6}} \:−\:\mathrm{2}{x}^{\mathrm{3}} } \:{dx} \\ $$

Question Number 33154 Answers: 0 Comments: 1

it is given that Σ_(r=1) ^n U_n = ((1+3^(2n+2) −2×5^(n+1) )/8) where U_n is the n^(th) term of a sequence find the simplified expression for U_n

$${it}\:{is}\:{given}\:{that}\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\:{U}_{{n}} =\:\frac{\mathrm{1}+\mathrm{3}^{\mathrm{2}{n}+\mathrm{2}} −\mathrm{2}×\mathrm{5}^{{n}+\mathrm{1}} }{\mathrm{8}} \\ $$$${where}\:{U}_{{n}} \:{is}\:{the}\:{n}^{{th}} \:{term}\:{of}\:{a}\:{sequence} \\ $$$${find}\:{the}\:{simplified}\:{expression}\:{for}\:{U}_{{n}} \\ $$

Question Number 33151 Answers: 0 Comments: 0

Question Number 33147 Answers: 2 Comments: 1

If x^m occurs in the expansion of (x + (1/x^2 ))^(2n) , the coefficient of x^m is

$$\mathrm{If}\:\:\:{x}^{{m}} \:\:\mathrm{occurs}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left({x}\:+\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)^{\mathrm{2}{n}} ,\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{{m}} \:\mathrm{is} \\ $$

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