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AllQuestion and Answers: Page 999

Question Number 119323 Answers: 1 Comments: 4

Question Number 119314 Answers: 1 Comments: 5

Question Number 119306 Answers: 3 Comments: 0

Question Number 119303 Answers: 3 Comments: 0

let x,y,z be positive real numbers such that x+y+z=1. Determine the minimum value of (1/x)+(4/y)+(9/z).

$$\:{let}\:{x},{y},{z}\:{be}\:{positive}\:{real}\:{numbers}\: \\ $$$${such}\:{that}\:{x}+{y}+{z}=\mathrm{1}.\:{Determine}\: \\ $$$${the}\:{minimum}\:{value}\:{of}\:\frac{\mathrm{1}}{{x}}+\frac{\mathrm{4}}{{y}}+\frac{\mathrm{9}}{{z}}. \\ $$

Question Number 119298 Answers: 1 Comments: 0

Question Number 119295 Answers: 1 Comments: 0

Let a and b non negative real numbers If sin x+acos x=b , express ∣ asin x−cos x∣ in terms of a and b.

$$\:{Let}\:{a}\:{and}\:{b}\:\:{non}\:{negative}\:{real}\:{numbers}\: \\ $$$${If}\:\mathrm{sin}\:{x}+{a}\mathrm{cos}\:{x}={b}\:,\:{express}\: \\ $$$$\mid\:{a}\mathrm{sin}\:{x}−\mathrm{cos}\:{x}\mid\:{in}\:{terms}\:{of}\:{a}\:{and}\:{b}. \\ $$$$ \\ $$

Question Number 119293 Answers: 1 Comments: 0

Question Number 119292 Answers: 2 Comments: 0

Question Number 119291 Answers: 2 Comments: 0

∫_0 ^( ∞) ((e^(−x) (x^(10) −1))/(ln(x))) dx

$$\int_{\mathrm{0}} ^{\:\infty} \frac{{e}^{−{x}} \left({x}^{\mathrm{10}} −\mathrm{1}\right)}{{ln}\left({x}\right)}\:{dx}\: \\ $$

Question Number 119290 Answers: 1 Comments: 0

(3x−y+1) dx +(6x+2y−3) dy = 0

$$\:\:\left(\mathrm{3}{x}−{y}+\mathrm{1}\right)\:{dx}\:+\left(\mathrm{6}{x}+\mathrm{2}{y}−\mathrm{3}\right)\:{dy}\:=\:\mathrm{0}\: \\ $$

Question Number 119282 Answers: 1 Comments: 0

... nice calculus... evaluate:: I:= ∫_0 ^( 1) li_2 (1−x^2 )dx=?? .m.n.1970.

$$\:\:\:\:\:\:\:\:...\:\:{nice}\:\:{calculus}... \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{evaluate}:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {li}_{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right){dx}=?? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.{m}.{n}.\mathrm{1970}. \\ $$$$\:\:\:\:\:\:\:\: \\ $$

Question Number 119280 Answers: 0 Comments: 0

Please more informations about this operator K_(p=1) ^∞ (......)

$$\:{Please}\:{more}\:{informations}\:{about}\:{this}\:{operator} \\ $$$$\:\:\underset{{p}=\mathrm{1}} {\overset{\infty} {{K}}}\left(......\right) \\ $$

Question Number 119318 Answers: 0 Comments: 0

find ∫_0 ^∞ ((lnx)/(x^4 +x^2 +2))dx

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{lnx}}{{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{2}}{dx} \\ $$

Question Number 119317 Answers: 0 Comments: 0

calculate ∫_0 ^(2π) (dθ/((x^2 −2cosθ x+1)^2 ))

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{{d}\theta}{\left({x}^{\mathrm{2}} −\mathrm{2}{cos}\theta\:{x}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 119316 Answers: 0 Comments: 0

((Σ_(n=1) ^∞ (1/n^n ))/(Σ_(n=1) ^∞ (−1)^(n+1) (1/n^n )))

$$\frac{\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{{n}} }}{\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} \frac{\mathrm{1}}{{n}^{{n}} }} \\ $$

Question Number 119315 Answers: 2 Comments: 0

Question Number 119266 Answers: 3 Comments: 2

solve (((√3)−1)/(sin x)) + (((√3)+1)/(cos x)) = 4(√2) where x∈ (0,(π/2))

$$\:{solve}\:\frac{\sqrt{\mathrm{3}}−\mathrm{1}}{\mathrm{sin}\:{x}}\:+\:\frac{\sqrt{\mathrm{3}}+\mathrm{1}}{\mathrm{cos}\:{x}}\:=\:\mathrm{4}\sqrt{\mathrm{2}} \\ $$$${where}\:{x}\in\:\left(\mathrm{0},\frac{\pi}{\mathrm{2}}\right) \\ $$

Question Number 119262 Answers: 3 Comments: 0

∫ (x^2 /( (√((4−x^2 )^5 )))) dx

$$\:\int\:\frac{{x}^{\mathrm{2}} }{\:\sqrt{\left(\mathrm{4}−{x}^{\mathrm{2}} \right)^{\mathrm{5}} }}\:{dx}\: \\ $$

Question Number 119257 Answers: 0 Comments: 0

Isomeri di posizione C_4 H_8 → ciclobutano e metilciclopropano C_5 H_(10) → ciclopentano, metilciclobutano, dimetilciclopropano, etilciclo propano isomeri configurazionali cis−trans dell′1,2 dimetilciclobutano Guardo il legame C_1 −C_2 CH_3 e^ gruppo dominante sull′H (MM=15 contro 1) isomeri configurazionali: isomeria dovuta all′impossibilita^ di rotazione completa intorno ai legami σ. Tabella pag. 53 per la prossima verifica Capitolo 3 Elettrofili e nucleofili Tipi di reazioni Carblcationi e carbanioni Effetto induttivo → tabella Soft e hard

$$\mathrm{Isomeri}\:\mathrm{di}\:\mathrm{posizione} \\ $$$$\mathrm{C}_{\mathrm{4}} \mathrm{H}_{\mathrm{8}} \rightarrow\:\mathrm{ciclobutano}\:\mathrm{e}\:\mathrm{metilciclopropano} \\ $$$$\mathrm{C}_{\mathrm{5}} \mathrm{H}_{\mathrm{10}} \rightarrow\:\mathrm{ciclopentano},\:\mathrm{metilciclobutano},\:\mathrm{dimetilciclopropano},\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{etilciclo}\:\mathrm{propano} \\ $$$$\mathrm{isomeri}\:\mathrm{configurazionali}\:\mathrm{cis}−\mathrm{trans}\:\mathrm{dell}'\mathrm{1},\mathrm{2}\:\mathrm{dimetilciclobutano} \\ $$$$\mathrm{Guardo}\:\mathrm{il}\:\mathrm{legame}\:\mathrm{C}_{\mathrm{1}} −\mathrm{C}_{\mathrm{2}} \\ $$$$\mathrm{CH}_{\mathrm{3}} \acute {\mathrm{e}}\:\mathrm{gruppo}\:\mathrm{dominante}\:\mathrm{sull}'\mathrm{H}\:\left(\mathrm{MM}=\mathrm{15}\:\mathrm{contro}\:\mathrm{1}\right) \\ $$$$\mathrm{isomeri}\:\mathrm{configurazionali}:\:\mathrm{isomeria}\:\mathrm{dovuta}\:\mathrm{all}'\mathrm{impossibilit}\acute {\mathrm{a}}\:\mathrm{di}\:\mathrm{rotazione}\: \\ $$$$\mathrm{completa}\:\mathrm{intorno}\:\mathrm{ai}\:\mathrm{legami}\:\sigma. \\ $$$$\mathrm{Tabella}\:\mathrm{pag}.\:\mathrm{53}\:\mathrm{per}\:\mathrm{la}\:\mathrm{prossima}\:\mathrm{verifica} \\ $$$$\mathrm{Capitolo}\:\mathrm{3}\: \\ $$$$\mathrm{Elettrofili}\:\mathrm{e}\:\mathrm{nucleofili} \\ $$$$\mathrm{Tipi}\:\mathrm{di}\:\mathrm{reazioni} \\ $$$$\mathrm{Carblcationi}\:\mathrm{e}\:\mathrm{carbanioni} \\ $$$$\mathrm{Effetto}\:\mathrm{induttivo}\:\rightarrow\:\mathrm{tabella} \\ $$$$\mathrm{Soft}\:\mathrm{e}\:\mathrm{hard} \\ $$

Question Number 119256 Answers: 0 Comments: 0

Determine ∫_(−(π/4)) ^( (π/4)) (cost+(√(1+t^2 sin^3 tcos^3 t))dt=?

$$\: \\ $$$$\:\:\:\:\:\:{Determine}\:\:\int_{−\frac{\pi}{\mathrm{4}}} ^{\:\frac{\pi}{\mathrm{4}}} \left({cost}+\sqrt{\mathrm{1}+{t}^{\mathrm{2}} {sin}^{\mathrm{3}} {tcos}^{\mathrm{3}} {t}}{dt}=?\right. \\ $$

Question Number 119253 Answers: 2 Comments: 0

Given three function f(x) ,g(x) and h(x). where f(x)=x^2 +x−2 and h(x)=x^2 +2x−1. If ((f(x))/(x+3)) ≤ ((g(x))/(x+3)) ≤ ((h(x))/(x+3)) , then the value of lim_(x→−1) g(x) = ?

$${Given}\:{three}\:{function}\:{f}\left({x}\right)\:,{g}\left({x}\right)\:{and}\:{h}\left({x}\right). \\ $$$${where}\:{f}\left({x}\right)={x}^{\mathrm{2}} +{x}−\mathrm{2}\:{and}\:{h}\left({x}\right)={x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{1}. \\ $$$${If}\:\frac{{f}\left({x}\right)}{{x}+\mathrm{3}}\:\leqslant\:\frac{{g}\left({x}\right)}{{x}+\mathrm{3}}\:\leqslant\:\frac{{h}\left({x}\right)}{{x}+\mathrm{3}}\:,\:{then}\:{the}\:{value}\:{of} \\ $$$$\underset{{x}\rightarrow−\mathrm{1}} {\mathrm{lim}}\:{g}\left({x}\right)\:=\:? \\ $$

Question Number 119250 Answers: 1 Comments: 5

Question Number 119246 Answers: 2 Comments: 0

Prove the following inequalities hold true ∀x∈R a)cos(cosx)>0 b)cos(sinx)>sin(cosx)

$$\mathrm{Prove}\:\mathrm{the}\:\mathrm{following}\:\:\mathrm{inequalities}\:\mathrm{hold} \\ $$$$\:\:\mathrm{true}\:\forall\mathrm{x}\in\mathrm{R} \\ $$$$\left.\mathrm{a}\right)\mathrm{cos}\left(\mathrm{cosx}\right)>\mathrm{0} \\ $$$$\left.\mathrm{b}\right)\mathrm{cos}\left(\mathrm{sinx}\right)>\mathrm{sin}\left(\mathrm{cosx}\right) \\ $$

Question Number 119241 Answers: 1 Comments: 0

675×54/100

$$\mathrm{675}×\mathrm{54}/\mathrm{100} \\ $$

Question Number 119240 Answers: 2 Comments: 0

find max and min value of f(x,y) = 4x^2 +8xy+9y^2 −8x−24y+4

$${find}\:{max}\:{and}\:{min}\:{value}\:{of}\: \\ $$$${f}\left({x},{y}\right)\:=\:\mathrm{4}{x}^{\mathrm{2}} +\mathrm{8}{xy}+\mathrm{9}{y}^{\mathrm{2}} −\mathrm{8}{x}−\mathrm{24}{y}+\mathrm{4}\: \\ $$

Question Number 119235 Answers: 1 Comments: 0

(D^3 +D^2 −4D−4)y = e^(4x)

$$\:\left({D}^{\mathrm{3}} +{D}^{\mathrm{2}} −\mathrm{4}{D}−\mathrm{4}\right){y}\:=\:{e}^{\mathrm{4}{x}} \\ $$

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