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Question Number 158272 Answers: 1 Comments: 0

Question Number 158271 Answers: 0 Comments: 0

Question Number 158270 Answers: 0 Comments: 0

82,1336,18670,240004,2933338,34666672,400000006,? is there a valid pattern for these numbers?

$$\mathrm{82},\mathrm{1336},\mathrm{18670},\mathrm{240004},\mathrm{2933338},\mathrm{34666672},\mathrm{400000006},? \\ $$$$\mathrm{is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{valid}\:\mathrm{pattern}\:\mathrm{for}\:\mathrm{these}\:\mathrm{numbers}? \\ $$

Question Number 158267 Answers: 0 Comments: 0

soit:F={(x,y,z)∈R^3 /x−y−2z} et G=Vect(0,1,1) determiner l′intersection de F et G

$${soit}:{F}=\left\{\left({x},{y},{z}\right)\in{R}^{\mathrm{3}} /{x}−{y}−\mathrm{2}{z}\right\}\:{et} \\ $$$${G}={Vect}\left(\mathrm{0},\mathrm{1},\mathrm{1}\right) \\ $$$${determiner}\:{l}'{intersection}\:{de}\:{F}\:{et}\:{G} \\ $$

Question Number 158259 Answers: 1 Comments: 1

Given x,y∈R^+ and ((x/5)+(y/3))((5/x)+(3/y))=139. If maximum and minimum of ((x+y)/( (√(xy)) )) is M and n respectively, then what the value of 3M−4n.

$${Given}\:{x},{y}\in\mathbb{R}^{+} \:{and}\:\left(\frac{{x}}{\mathrm{5}}+\frac{{y}}{\mathrm{3}}\right)\left(\frac{\mathrm{5}}{{x}}+\frac{\mathrm{3}}{{y}}\right)=\mathrm{139}. \\ $$$$\:{If}\:{maximum}\:{and}\:{minimum} \\ $$$$\:{of}\:\frac{{x}+{y}}{\:\sqrt{{xy}}\:}\:{is}\:{M}\:{and}\:{n}\:{respectively}, \\ $$$${then}\:{what}\:{the}\:{value}\:{of}\:\mathrm{3}{M}−\mathrm{4}{n}. \\ $$

Question Number 158252 Answers: 0 Comments: 0

Question Number 158625 Answers: 0 Comments: 1

EI(∂^4 y/∂x^4 )+ρS(∂^2 y/∂t^2 )=0 (1) y(x,0)=U_0 (x) (∂y/∂t)(x,0)=V_0 (x) ; EI(∂^2 y/∂x^2 )(0,t)=EI(∂^2 y/∂x^2 )(L,t)=0

$${EI}\frac{\partial^{\mathrm{4}} {y}}{\partial{x}^{\mathrm{4}} }+\rho{S}\frac{\partial^{\mathrm{2}} {y}}{\partial{t}^{\mathrm{2}} }=\mathrm{0}\:\:\:\left(\mathrm{1}\right) \\ $$$${y}\left({x},\mathrm{0}\right)={U}_{\mathrm{0}} \left({x}\right) \\ $$$$\frac{\partial{y}}{\partial{t}}\left({x},\mathrm{0}\right)={V}_{\mathrm{0}} \left({x}\right)\:\:\:\:\:\:;\:{EI}\frac{\partial^{\mathrm{2}} {y}}{\partial{x}^{\mathrm{2}} }\left(\mathrm{0},{t}\right)={EI}\frac{\partial^{\mathrm{2}} {y}}{\partial{x}^{\mathrm{2}} }\left({L},{t}\right)=\mathrm{0} \\ $$

Question Number 158245 Answers: 1 Comments: 0

Prove that: (((x-1)^2 )/x) + ((x+1)/( (√(x^2 +1)))) ≥ (√2) ; ∀x>0

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\frac{\left(\mathrm{x}-\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{x}}\:+\:\frac{\mathrm{x}+\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}}\:\geqslant\:\sqrt{\mathrm{2}}\:\:;\:\:\forall\mathrm{x}>\mathrm{0} \\ $$$$ \\ $$

Question Number 158241 Answers: 0 Comments: 0

Prove that: (((x-1)^2 )/x) + ((x+1)/( (√(x^2 +1)))) ≥ 2 ; ∀x>0

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\frac{\left(\mathrm{x}-\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{x}}\:+\:\frac{\mathrm{x}+\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}}\:\geqslant\:\mathrm{2}\:\:;\:\:\forall\mathrm{x}>\mathrm{0} \\ $$

Question Number 158240 Answers: 1 Comments: 0

Prove that 5 divide n(4n^2 + 1)(6n^2 + 1) for any natural number n

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{5}\:\mathrm{divide} \\ $$$$\mathrm{n}\left(\mathrm{4n}^{\mathrm{2}} \:+\:\mathrm{1}\right)\left(\mathrm{6n}^{\mathrm{2}} \:+\:\mathrm{1}\right) \\ $$$$\mathrm{for}\:\mathrm{any}\:\mathrm{natural}\:\mathrm{number}\:\boldsymbol{\mathrm{n}} \\ $$

Question Number 158274 Answers: 1 Comments: 0

Solve for complex numbers: x^4 + (1 + i)x^3 + 2ix^2 + (i - 1)x - 1 = 0

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{complex}\:\mathrm{numbers}: \\ $$$$\mathrm{x}^{\mathrm{4}} \:+\:\left(\mathrm{1}\:+\:\boldsymbol{\mathrm{i}}\right)\boldsymbol{\mathrm{x}}^{\mathrm{3}} \:+\:\mathrm{2}\boldsymbol{\mathrm{ix}}^{\mathrm{2}} \:+\:\left(\boldsymbol{\mathrm{i}}\:-\:\mathrm{1}\right)\boldsymbol{\mathrm{x}}\:-\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$ \\ $$

Question Number 158230 Answers: 0 Comments: 0

∫(1/(1+ln x))dx=?

$$\int\frac{\mathrm{1}}{\mathrm{1}+\mathrm{ln}\:{x}}{dx}=? \\ $$

Question Number 158237 Answers: 0 Comments: 1

Question Number 158220 Answers: 0 Comments: 0

source: myself x^5 +3cx^2 −x−5c=0

$$\:\:\:{source}:\:{myself} \\ $$$$\:{x}^{\mathrm{5}} +\mathrm{3}{cx}^{\mathrm{2}} −{x}−\mathrm{5}{c}=\mathrm{0} \\ $$

Question Number 158228 Answers: 1 Comments: 0

∫((5x^3 −3x^2 +7x−3)/((x^2 +1)^2 ))dx Solve by first finding the partial fraction

$$\int\frac{\mathrm{5}{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{7}{x}−\mathrm{3}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$$${Solve}\:{by}\:{first}\:{finding}\:{the}\:{partial} \\ $$$${fraction} \\ $$

Question Number 158209 Answers: 1 Comments: 0

Question Number 158207 Answers: 1 Comments: 0

Question Number 158205 Answers: 0 Comments: 0

(1) lim_(x→0) (((e^x −1)sin x+tan^3 x)/(arctan x ln (1+4x)+4arcsin^4 x)) (2) lim_(x→0) ((1−cos x+ln (1+tan^2 2x)+2arcsin^3 x)/(1−cos 4x+sin^2 x))

$$\left(\mathrm{1}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left({e}^{{x}} −\mathrm{1}\right)\mathrm{sin}\:{x}+\mathrm{tan}\:^{\mathrm{3}} {x}}{\mathrm{arctan}\:{x}\:\mathrm{ln}\:\left(\mathrm{1}+\mathrm{4}{x}\right)+\mathrm{4arcsin}^{\mathrm{4}} \:{x}}\: \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:{x}+\mathrm{ln}\:\left(\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} \mathrm{2}{x}\right)+\mathrm{2arcsin}\:^{\mathrm{3}} \:{x}}{\mathrm{1}−\mathrm{cos}\:\mathrm{4}{x}+\mathrm{sin}\:^{\mathrm{2}} {x}} \\ $$

Question Number 158204 Answers: 2 Comments: 0

lim_(x→∞) (sin (√(x+1))−sin (√(x ))) =?

$$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{sin}\:\sqrt{{x}+\mathrm{1}}−\mathrm{sin}\:\sqrt{{x}\:}\right)\:=? \\ $$

Question Number 158203 Answers: 0 Comments: 0

lim_(n→∞) Σ_(k=1) ^n (1/n).e^((2k+1)/k) =?

$$\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{{n}}.{e}^{\frac{\mathrm{2}{k}+\mathrm{1}}{{k}}} \:=? \\ $$

Question Number 158190 Answers: 0 Comments: 1

∫((5x^3 −3x^2 +7x−3)/((x^2 +1)^2 ))dx Solve by first giving the partial functions

$$\int\frac{\mathrm{5}{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{7}{x}−\mathrm{3}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx}\:{Solve}\:{by}\: \\ $$$${first}\:{giving}\:{the}\:{partial}\:{functions}\: \\ $$

Question Number 158176 Answers: 1 Comments: 0

∫{((x^2 −x−21)/(2x^3 −x^2 +8x−4))}dx

$$\int\left\{\frac{{x}^{\mathrm{2}} −{x}−\mathrm{21}}{\mathrm{2}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{8}{x}−\mathrm{4}}\right\}{dx}\: \\ $$

Question Number 158175 Answers: 1 Comments: 1

lim_(x→+∞ ) ((sinx+x)/(3+2sinx))=?

$$\underset{{x}\rightarrow+\infty\:} {{lim}}\frac{{sinx}+{x}}{\mathrm{3}+\mathrm{2}{sinx}}=? \\ $$

Question Number 158173 Answers: 0 Comments: 0

simplify the expression (1+sin 𝛗)/(5+3tan 𝛗−4cos 𝛗) using small angles approximation up to the term containing φ^2

$$\mathrm{simplify}\:\mathrm{the}\:\mathrm{expression}\:\left(\mathrm{1}+\mathrm{sin}\:\boldsymbol{\phi}\right)/\left(\mathrm{5}+\mathrm{3tan}\:\boldsymbol{\phi}−\mathrm{4cos}\:\boldsymbol{\phi}\right)\:\mathrm{using}\:\mathrm{small}\:\mathrm{angles}\:\mathrm{approximation}\:\mathrm{up}\:\mathrm{to}\:\mathrm{the}\:\mathrm{term}\:\mathrm{containing}\:\phi^{\mathrm{2}} \\ $$

Question Number 158166 Answers: 0 Comments: 1

If f((x/3))=((f(x))/2) and f(1−x)=1−f(x). find f(((173)/(1993))).

$$\:{If}\:{f}\left(\frac{{x}}{\mathrm{3}}\right)=\frac{{f}\left({x}\right)}{\mathrm{2}}\:{and}\:{f}\left(\mathrm{1}−{x}\right)=\mathrm{1}−{f}\left({x}\right). \\ $$$${find}\:{f}\left(\frac{\mathrm{173}}{\mathrm{1993}}\right). \\ $$

Question Number 158157 Answers: 0 Comments: 0

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