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Question Number 33258 Answers: 0 Comments: 0

if (1/(1+cosx)) = (a_0 /2) +Σ_(n≥1) a_n cos(nx) calculate a_0 and a_n

$${if}\:\:\:\frac{\mathrm{1}}{\mathrm{1}+{cosx}}\:=\:\frac{{a}_{\mathrm{0}} }{\mathrm{2}}\:+\sum_{{n}\geqslant\mathrm{1}} {a}_{{n}} {cos}\left({nx}\right)\:{calculate}\:{a}_{\mathrm{0}} \\ $$$${and}\:{a}_{{n}} \\ $$

Question Number 33257 Answers: 0 Comments: 1

let g(x)= (1/(1+x^4 )) 1) find g^((n)) (x) 2) calculate g^((n)) (0) 3) if g(x)=Σ u_n x^n find the sequence u_n

$${let}\:{g}\left({x}\right)=\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{4}} } \\ $$$$\left.\mathrm{1}\right)\:{find}\:{g}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{if}\:{g}\left({x}\right)=\Sigma\:{u}_{{n}} \:{x}^{{n}} \:\:\:{find}\:{the}\:{sequence}\:{u}_{{n}} \\ $$

Question Number 33256 Answers: 0 Comments: 1

let f(x) = (1/(1+x^2 )) 1) calculate f^((n)) (x) 2) find f^((n)) (0) 3) developp f(x) at integr serie.

$${let}\:{f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\left({x}\right)\:{at}\:{integr}\:{serie}. \\ $$$$ \\ $$

Question Number 33255 Answers: 0 Comments: 2

if the roots of the equation 3x^2 +5x+2=0 are (α+β)(αβ) then the value of p if x^2 + px − 6=0 is?

$${if}\:{the}\:{roots}\:{of}\:{the}\:{equation}\: \\ $$$$\:\:\mathrm{3}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{2}=\mathrm{0}\:{are}\:\left(\alpha+\beta\right)\left(\alpha\beta\right) \\ $$$${then}\:{the}\:{value}\:{of}\:{p}\:{if}\:{x}^{\mathrm{2}} +\:{px}\:−\:\mathrm{6}=\mathrm{0} \\ $$$${is}? \\ $$

Question Number 33252 Answers: 0 Comments: 1

if α and β are roots of the equation x^2 +px + q=0 then the value p and q when x^2 + 3x + 2=0 has same roots are?

$${if}\:\alpha\:{and}\:\beta\:{are}\:{roots}\:{of}\:{the}\:{equation} \\ $$$$\:{x}^{\mathrm{2}} +{px}\:+\:{q}=\mathrm{0} \\ $$$${then}\:{the}\:{value}\:{p}\:{and}\:{q}\:{when}\: \\ $$$$\:\:{x}^{\mathrm{2}} +\:\mathrm{3}{x}\:+\:\mathrm{2}=\mathrm{0}\:{has}\:{same}\:{roots}\:{are}? \\ $$

Question Number 33240 Answers: 0 Comments: 3

Question Number 33239 Answers: 1 Comments: 0

Question Number 33230 Answers: 1 Comments: 0

how many ways can the word MOGGOMBABA be arranged hence find S_∞ of a sequence a,ar,ar^2 in integral 1,(√2) , 2,...

$${how}\:{many}\:{ways}\:{can}\:{the}\:{word}\: \\ $$$$\:\:\:\:{MOGGOMBABA}\: \\ $$$${be}\:{arranged}\:{hence}\:{find}\:{S}_{\infty} \:{of}\:{a}\: \\ $$$${sequence}\:{a},{ar},{ar}^{\mathrm{2}} \:{in}\:{integral}\: \\ $$$$\:\:\mathrm{1},\sqrt{\mathrm{2}}\:,\:\mathrm{2},... \\ $$

Question Number 33222 Answers: 0 Comments: 0

let give n ≥3 integr calculate I_n = ∫_(−∞) ^(+∞) (dx/(1+x +x^2 +....+x^(n−1) ))

$${let}\:{give}\:{n}\:\geqslant\mathrm{3}\:{integr}\:\:{calculate} \\ $$$${I}_{{n}} =\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\frac{{dx}}{\mathrm{1}+{x}\:+{x}^{\mathrm{2}} \:+....+{x}^{{n}−\mathrm{1}} } \\ $$

Question Number 33223 Answers: 0 Comments: 0

let A_n =∫_(−∞) ^(+∞) (e^(iπx) /(1+x+x^2 +...x^(n−1) )) with n≥3 integr find the value of A_n .

$${let}\:\:{A}_{{n}} \:=\int_{−\infty} ^{+\infty} \:\:\:\frac{{e}^{{i}\pi{x}} }{\mathrm{1}+{x}+{x}^{\mathrm{2}} \:+...{x}^{{n}−\mathrm{1}} }\:\:{with}\:{n}\geqslant\mathrm{3}\:{integr} \\ $$$${find}\:{the}\:{value}\:{of}\:{A}_{{n}} \:. \\ $$

Question Number 33218 Answers: 1 Comments: 0

find the angle bisector 3x^2 +4xy−5y^2 =0

$$\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{angle}}\:\boldsymbol{\mathrm{bisector}} \\ $$$$\:\mathrm{3}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{4}\boldsymbol{{xy}}−\mathrm{5}\boldsymbol{{y}}^{\mathrm{2}} =\mathrm{0} \\ $$

Question Number 33217 Answers: 0 Comments: 7

Question Number 33216 Answers: 1 Comments: 0

Question Number 33214 Answers: 0 Comments: 8

Question Number 33211 Answers: 0 Comments: 0

find lim_(x→+∞) x e^(−x^2 ) ∫_(x−1) ^x e^t^2 dt .

$${find}\:{lim}_{{x}\rightarrow+\infty} \:\:\:{x}\:{e}^{−{x}^{\mathrm{2}} } \:\:\int_{{x}−\mathrm{1}} ^{{x}} \:{e}^{{t}^{\mathrm{2}} } {dt}\:. \\ $$

Question Number 33210 Answers: 0 Comments: 0

find lim_(x→+∞) x e^(−x^2 ) ∫^(x−1) _0 e^t^2 dt

$${find}\:\:{lim}_{{x}\rightarrow+\infty} \:\:{x}\:{e}^{−{x}^{\mathrm{2}} } \:\:\:\underset{\mathrm{0}} {\int}^{{x}−\mathrm{1}} \:\:{e}^{{t}^{\mathrm{2}} } \:{dt} \\ $$

Question Number 33209 Answers: 0 Comments: 0

solve the system x^′ =ay and y^′ =−ax . afrom R ,a≠0

$${solve}\:{the}\:{system}\:\:{x}^{'} \:={ay}\:{and}\:{y}^{'} \:=−{ax}\:.\:{afrom}\:{R}\:\:,{a}\neq\mathrm{0} \\ $$

Question Number 33208 Answers: 0 Comments: 0

solve the d.e. x^(′′) (t) +3x^′ (t) +2 x(t) = (1/(1+e^t ))

$${solve}\:{the}\:{d}.{e}.\:{x}^{''} \left({t}\right)\:+\mathrm{3}{x}^{'} \left({t}\right)\:+\mathrm{2}\:{x}\left({t}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}+{e}^{{t}} } \\ $$

Question Number 33207 Answers: 0 Comments: 0

Question Number 33204 Answers: 0 Comments: 1

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

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

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

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

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