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Question Number 74322 Answers: 1 Comments: 0

Let k = (((xy + yz + zx)(x + y + z))/((x + y)(y + z)(z + x))) Find the minimum and maximum value of k .

$${Let}\:\: \\ $$$${k}\:\:=\:\:\frac{\left({xy}\:+\:{yz}\:+\:{zx}\right)\left({x}\:+\:{y}\:+\:{z}\right)}{\left({x}\:+\:{y}\right)\left({y}\:+\:{z}\right)\left({z}\:+\:{x}\right)} \\ $$$${Find}\:\:{the}\:\:{minimum}\:\:{and}\:\:{maximum}\:\:{value}\:\:{of}\:\:\:{k}\:. \\ $$

Question Number 74320 Answers: 0 Comments: 0

∫_0 ^x x e^x (cos e^x )e^x dx

$$\int_{\mathrm{0}} ^{{x}} {x}\:{e}^{{x}} \left(\mathrm{cos}\:\:{e}^{{x}} \right){e}^{{x}} {dx} \\ $$

Question Number 74359 Answers: 0 Comments: 1

Question Number 74358 Answers: 0 Comments: 6

Question Number 74308 Answers: 1 Comments: 0

Question Number 74301 Answers: 1 Comments: 0

Prove that S={(x,y,z)∈R^3 \ x^2 +y^2 =z^2 } is a surface and find out if possible the tangent plan in O(0,0,0).

$${Prove}\:{that}\:\:{S}=\left\{\left({x},{y},{z}\right)\in\mathbb{R}^{\mathrm{3}} \backslash\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={z}^{\mathrm{2}} \:\right\}\:{is}\:{a}\:{surface}\: \\ $$$${and}\:{find}\:{out}\:{if}\:{possible}\:{the}\:{tangent}\:{plan}\:{in}\:{O}\left(\mathrm{0},\mathrm{0},\mathrm{0}\right). \\ $$

Question Number 74300 Answers: 1 Comments: 0

Let consider γ :I→R^2 a parametric curve 1)Prove that if a<b and γ(a)≠γ(b) then there exist t_0 ∈]a,b[ such as γ′(t_0 ) is colinear to γ(b)−γ(a) 2)Show that if γ is regular and the function f :I→R t→f(t)=∣∣γ(t)−O(0,0) ∣∣ is maximal in t_0 ∈I Then ∣K_γ (t_0 )∣≥(1/(f(t_0 )))

$${Let}\:{consider}\:\:\gamma\:\::{I}\rightarrow\mathbb{R}^{\mathrm{2}} \:\:{a}\:{parametric}\:{curve}\: \\ $$$$\left.\mathrm{1}\left.\right){Prove}\:{that}\:{if}\:\:{a}<{b}\:\:{and}\:\:\gamma\left({a}\right)\neq\gamma\left({b}\right)\:{then}\:{there}\:{exist}\:\:{t}_{\mathrm{0}} \in\right]{a},{b}\left[\:\:\right. \\ $$$${such}\:{as}\:\:\gamma'\left({t}_{\mathrm{0}} \right)\:\:{is}\:{colinear}\:{to}\:\gamma\left({b}\right)−\gamma\left({a}\right)\: \\ $$$$\left.\mathrm{2}\right){Show}\:{that}\:{if}\:\:\gamma\:{is}\:{regular}\:{and}\:{the}\:\:{function}\:{f}\::{I}\rightarrow\mathbb{R}\:\:\:\:{t}\rightarrow{f}\left({t}\right)=\mid\mid\gamma\left({t}\right)−{O}\left(\mathrm{0},\mathrm{0}\right)\:\mid\mid\:\:{is}\:{maximal}\:{in}\:{t}_{\mathrm{0}} \in{I} \\ $$$${Then}\:\:\mid{K}_{\gamma} \left({t}_{\mathrm{0}} \right)\mid\geqslant\frac{\mathrm{1}}{{f}\left({t}_{\mathrm{0}} \right)} \\ $$

Question Number 74293 Answers: 0 Comments: 2

Question Number 74284 Answers: 2 Comments: 4

Question Number 74280 Answers: 2 Comments: 5

Let consider α : I→R^2 a parametric curve defined as ∀ t∈I α(t)=(((t^2 −1)/(t^3 −1)) ,((2t)/(t^3 −1))) Prove that for a,b,c∈I α(a),α(b),α(c) are on the same lign iff abc=a+b+c+1

$${Let}\:\:{consider}\:\alpha\::\:{I}\rightarrow\mathbb{R}^{\mathrm{2}} \:\:{a}\:{parametric}\:{curve}\:{defined}\:{as} \\ $$$$\forall\:{t}\in{I}\:\:\:\alpha\left({t}\right)=\left(\frac{{t}^{\mathrm{2}} −\mathrm{1}}{{t}^{\mathrm{3}} −\mathrm{1}}\:,\frac{\mathrm{2}{t}}{{t}^{\mathrm{3}} −\mathrm{1}}\right)\: \\ $$$${Prove}\:{that}\:{for}\:{a},{b},{c}\in{I}\:\:\: \\ $$$$\:\:\alpha\left({a}\right),\alpha\left({b}\right),\alpha\left({c}\right)\:{are}\:{on}\:{the}\:{same}\:{lign}\:{iff}\:\:{abc}={a}+{b}+{c}+\mathrm{1} \\ $$

Question Number 74274 Answers: 1 Comments: 0

Question Number 74267 Answers: 1 Comments: 0

1 what is the order and the degree of the differential equation (d^3 Z/dt^3 ) +((dZ/dt))^4 − y^5 =e^(−2x) . 2) 2x(d^5 y/dx^5 ) + 5x^2 ((dy/dx) )^4 − xy^2 = 0.

$$\mathrm{1}\:\:{what}\:{is}\:{the}\:{order}\:{and}\:{the}\:{degree}\:{of}\:{the}\:{differential}\:{equation} \\ $$$$\frac{{d}^{\mathrm{3}} {Z}}{{dt}^{\mathrm{3}} }\:+\left(\frac{{dZ}}{{dt}}\right)^{\mathrm{4}} \:−\:{y}^{\mathrm{5}} \:={e}^{−\mathrm{2}{x}} . \\ $$$$\left.\mathrm{2}\right)\:\:\mathrm{2}{x}\frac{{d}^{\mathrm{5}} {y}}{{dx}^{\mathrm{5}} }\:+\:\mathrm{5}{x}^{\mathrm{2}} \:\left(\frac{{dy}}{{dx}}\:\right)^{\mathrm{4}} \:−\:{xy}^{\mathrm{2}} \:=\:\mathrm{0}. \\ $$

Question Number 74266 Answers: 0 Comments: 0

please kindly help me with the solutions to these question?very urgent please (1) if dy=x^3 dx. find the equation of y in terms of x if the curve passes through (1,1) 2) Given that the volume v(t) of cell at a time t changes according to ((dV(t))/dt)= sin t, with v(t)=4. find v(t) 3) Given (dP/dt) + 3P = 0. determine P (t) if p(0)= 4 4) Radium decomposes at a rate proportion to the amount present. if the half−life of the radium is 1000 years. what is the percentage lost in 100 years? 5) Calculate the pressure of a gas after phase transition at 171°K from 101.3kPa pressure at 472°K taking R = 0.1886kJ\kgK and L = 35.73kg

$${please}\:{kindly}\:{help}\:{me}\:{with}\:{the}\:{solutions}\:{to}\:{these}\:{question}?{very}\:{urgent}\:{please}\:\left(\mathrm{1}\right)\:{if}\:{dy}={x}^{\mathrm{3}} {dx}.\:{find}\:{the}\:{equation}\:{of}\:{y}\:{in}\:{terms}\:{of}\:{x} \\ $$$$\:{if}\:{the}\:{curve}\:{passes}\:{through}\:\left(\mathrm{1},\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right)\:{Given}\:{that}\:{the}\:{volume}\:{v}\left({t}\right)\:{of}\:{cell}\:{at}\:{a}\:{time}\:{t}\:{changes}\:{according}\:{to} \\ $$$$\frac{{dV}\left({t}\right)}{{dt}}=\:{sin}\:{t},\:{with}\:{v}\left({t}\right)=\mathrm{4}.\:{find}\:{v}\left({t}\right) \\ $$$$\left.\mathrm{3}\right)\:{Given}\:\frac{{dP}}{{dt}}\:+\:\mathrm{3}{P}\:=\:\mathrm{0}.\:{determine}\:{P}\:\left({t}\right)\: \\ $$$${if}\:{p}\left(\mathrm{0}\right)=\:\mathrm{4} \\ $$$$\left.\mathrm{4}\right)\:{Radium}\:{decomposes}\:{at}\:{a}\:{rate}\:{proportion}\:{to}\:{the}\:{amount}\: \\ $$$${present}.\:{if}\:{the}\:{half}−{life}\:{of}\:{the}\:{radium}\:{is} \\ $$$$\mathrm{1000}\:{years}.\:{what}\:{is}\:{the}\:{percentage}\:{lost}\:{in}\:\mathrm{100}\:{years}? \\ $$$$\left.\mathrm{5}\right)\:{Calculate}\:{the}\:{pressure}\:{of}\:{a}\:{gas}\:{after}\:{phase} \\ $$$${transition}\:{at}\:\mathrm{171}°{K}\:{from}\:\mathrm{101}.\mathrm{3}{kPa} \\ $$$${pressure}\:{at}\:\mathrm{472}°{K}\:{taking}\:{R}\:=\:\mathrm{0}.\mathrm{1886}{kJ}\backslash{kgK}\:{and}\:{L}\:=\:\mathrm{35}.\mathrm{73}{kg} \\ $$

Question Number 74265 Answers: 1 Comments: 0

Determine the values of m∈R for which the function f(x)=(1/(√(2x^2 −mx+m))) is the set of real numbers.

$${Determine}\:{the}\:{values}\:{of}\:{m}\in\mathbb{R}\:{for}\: \\ $$$${which}\:{the}\:{function}\:{f}\left({x}\right)=\frac{\mathrm{1}}{\sqrt{\mathrm{2}{x}^{\mathrm{2}} −{mx}+{m}}} \\ $$$${is}\:{the}\:{set}\:{of}\:{real}\:{numbers}. \\ $$

Question Number 74264 Answers: 0 Comments: 1

∫_0 ^x xe^x sin e^x e^x dx

$$\int_{\mathrm{0}} ^{{x}} {xe}^{{x}} \mathrm{sin}\:{e}^{{x}} {e}^{{x}} {dx} \\ $$

Question Number 74263 Answers: 0 Comments: 1

∫_0 ^x e^x cos e^x e^x dx

$$\int_{\mathrm{0}} ^{{x}} {e}^{{x}} \mathrm{cos}\:{e}^{{x}} {e}^{{x}} {dx} \\ $$

Question Number 74246 Answers: 2 Comments: 0

Question Number 74244 Answers: 2 Comments: 0

Find x x^(log_(4 ) (√x)) =x^(log_4 x) −2

$${Find}\:{x} \\ $$$${x}^{{log}_{\mathrm{4}\:} \sqrt{{x}}} ={x}^{{log}_{\mathrm{4}} {x}} −\mathrm{2} \\ $$

Question Number 74240 Answers: 1 Comments: 3

Question Number 74235 Answers: 3 Comments: 0

Question Number 74234 Answers: 0 Comments: 0

f(x)=(1/((4x^3 ))^(1/5) ) find f^ ′(x) with using lim_(h→0) ((f(x+h)−f(x))/h)

$${f}\left({x}\right)=\frac{\mathrm{1}}{\sqrt[{\mathrm{5}}]{\mathrm{4}{x}^{\mathrm{3}} }} \\ $$$$ \\ $$$${find}\:{f}^{\:} '\left({x}\right) \\ $$$$ \\ $$$${with}\:{using}\:\underset{{h}\rightarrow\mathrm{0}} {{lim}}\frac{{f}\left({x}+{h}\right)−{f}\left({x}\right)}{{h}} \\ $$

Question Number 74231 Answers: 1 Comments: 2

Question Number 74226 Answers: 0 Comments: 0

Question Number 74225 Answers: 1 Comments: 0

let p(x)=(1+jx)^n −(1−jx)^n with j=e^((i2π)/3) 1) determine the roots of p(x) and factorize P(x) inside C[x] 2) decompose the fraction F(x)=(1/(p(x)))

$${let}\:{p}\left({x}\right)=\left(\mathrm{1}+{jx}\right)^{{n}} −\left(\mathrm{1}−{jx}\right)^{{n}} \:\:{with}\:{j}={e}^{\frac{{i}\mathrm{2}\pi}{\mathrm{3}}} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{the}\:{roots}\:{of}\:{p}\left({x}\right)\:{and}\:{factorize}\:{P}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{2}\right)\:{decompose}\:{the}\:{fraction}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{p}\left({x}\right)} \\ $$

Question Number 74224 Answers: 1 Comments: 2

find ∫ (x^2 +1)^(1/4) cos((1/2)arctan((1/x)))dx and ∫ (x^2 +1)^(1/4) sin((1/2)arctan((1/x)))dx

$${find}\:\int\:\:\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} \:{cos}\left(\frac{\mathrm{1}}{\mathrm{2}}{arctan}\left(\frac{\mathrm{1}}{{x}}\right)\right){dx}\:\:{and} \\ $$$$\int\:\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} {sin}\left(\frac{\mathrm{1}}{\mathrm{2}}{arctan}\left(\frac{\mathrm{1}}{{x}}\right)\right){dx} \\ $$

Question Number 74223 Answers: 1 Comments: 0

calculate f(a)=∫_0 ^1 (√(x^2 +ax+1))dx and g(a)=∫_0 ^1 ((xdx)/(√(x^2 +ax+1))) with ∣a∣<2 2)find the value of ∫_0 ^1 (√(x^2 +(√2)x+1))dx and ∫_0 ^1 ((xdx)/(√(x^2 +(√2)x+1)))

$${calculate}\:\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}^{\mathrm{2}} +{ax}+\mathrm{1}}{dx}\:\:\:{and}\:{g}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{xdx}}{\sqrt{{x}^{\mathrm{2}} +{ax}+\mathrm{1}}} \\ $$$${with}\:\:\mid{a}\mid<\mathrm{2} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}^{\mathrm{2}} +\sqrt{\mathrm{2}}{x}+\mathrm{1}}{dx}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{xdx}}{\sqrt{{x}^{\mathrm{2}} +\sqrt{\mathrm{2}}{x}+\mathrm{1}}} \\ $$

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