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Question Number 154400 Answers: 1 Comments: 0

x(√y) - y(√x) = 82 x(√x) + y(√y) = 83 (9/5) ∙ (x + y) = ?

$$\mathrm{x}\sqrt{\mathrm{y}}\:-\:\mathrm{y}\sqrt{\mathrm{x}}\:=\:\mathrm{82} \\ $$$$\mathrm{x}\sqrt{\mathrm{x}}\:+\:\mathrm{y}\sqrt{\mathrm{y}}\:=\:\mathrm{83} \\ $$$$\frac{\mathrm{9}}{\mathrm{5}}\:\centerdot\:\left(\mathrm{x}\:+\:\mathrm{y}\right)\:=\:? \\ $$

Question Number 154398 Answers: 1 Comments: 0

Question Number 154395 Answers: 1 Comments: 1

Question Number 154396 Answers: 1 Comments: 0

Question Number 154390 Answers: 1 Comments: 1

lim_(x→2) ((x^2 e^x −4e^2 )/(x−2)) ?

$$\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} {e}^{{x}} −\mathrm{4}{e}^{\mathrm{2}} }{{x}−\mathrm{2}}\:? \\ $$

Question Number 154385 Answers: 2 Comments: 0

if (x)^(1/3) −((x−36))^(1/3) =3 find x−(1/x)

$${if}\:\:\:\sqrt[{\mathrm{3}}]{{x}}−\sqrt[{\mathrm{3}}]{{x}−\mathrm{36}}=\mathrm{3}\:\:\:\:\:\:{find}\:\:\:\:{x}−\frac{\mathrm{1}}{{x}} \\ $$

Question Number 154383 Answers: 0 Comments: 0

Question Number 154384 Answers: 1 Comments: 0

If x;y;z>0 then: ((4x^2 )/(x+y)) + ((8y^2 )/(y+z)) + ((4z^2 )/(z+x)) ≥ 2x + 5y + z

$$\mathrm{If}\:\:\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:\:\mathrm{then}: \\ $$$$\frac{\mathrm{4x}^{\mathrm{2}} }{\mathrm{x}+\mathrm{y}}\:+\:\frac{\mathrm{8y}^{\mathrm{2}} }{\mathrm{y}+\mathrm{z}}\:+\:\frac{\mathrm{4z}^{\mathrm{2}} }{\mathrm{z}+\mathrm{x}}\:\geqslant\:\mathrm{2x}\:+\:\mathrm{5y}\:+\:\mathrm{z} \\ $$

Question Number 154380 Answers: 1 Comments: 0

Question Number 154372 Answers: 0 Comments: 0

If a;b;c>0 and a^2 +b^2 +c^2 =3 Then prove that: Σ (a^3 /(b^2 + b + bc)) ≥ 1

$$\mathrm{If}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} =\mathrm{3} \\ $$$$\mathrm{Then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\Sigma\:\frac{\mathrm{a}^{\mathrm{3}} }{\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{b}\:+\:\mathrm{bc}}\:\geqslant\:\mathrm{1} \\ $$

Question Number 154368 Answers: 0 Comments: 0

Question Number 154365 Answers: 0 Comments: 0

Question Number 154359 Answers: 1 Comments: 0

If f(0)=1, f(2)=3, f ′(2)=5, find the value of ∫_0 ^( 1) x f′′(2x) dx.

$$\mathrm{If}\:{f}\left(\mathrm{0}\right)=\mathrm{1},\:{f}\left(\mathrm{2}\right)=\mathrm{3},\:{f}\:'\left(\mathrm{2}\right)=\mathrm{5}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}\:{f}''\left(\mathrm{2}{x}\right)\:{dx}. \\ $$

Question Number 154353 Answers: 1 Comments: 4

Question Number 154352 Answers: 0 Comments: 0

∫(x^(n−1) /(x^(3n+1) (x^n −1)))dx=?

$$\:\int\frac{{x}^{{n}−\mathrm{1}} }{{x}^{\mathrm{3}{n}+\mathrm{1}} \left({x}^{{n}} −\mathrm{1}\right)}{dx}=? \\ $$

Question Number 154351 Answers: 3 Comments: 0

∫_(−1) ^( 0) ((x−1)/( (√(x^2 −4x+3)) )) dx =?

$$\int_{−\mathrm{1}} ^{\:\mathrm{0}} \:\frac{{x}−\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{3}}\:}\:{dx}\:=? \\ $$

Question Number 154343 Answers: 1 Comments: 0

Question Number 154337 Answers: 2 Comments: 0

etudier la continuite, et derivabilite: x^2 sin((1/x)) si≠0 et f(0)=0

$${etudier}\:{la}\:{continuite},\:{et}\:{derivabilite}: \\ $$$${x}^{\mathrm{2}} {sin}\left(\frac{\mathrm{1}}{{x}}\right)\:{si}\neq\mathrm{0}\:{et}\:{f}\left(\mathrm{0}\right)=\mathrm{0} \\ $$

Question Number 154334 Answers: 3 Comments: 1

the n^(th) term of 1 , 2, 6, 24, 120 ........ is?

$${the}\:{n}^{{th}} \:{term}\:{of} \\ $$$$\mathrm{1}\:,\:\mathrm{2},\:\mathrm{6},\:\mathrm{24},\:\mathrm{120}\:........\:{is}? \\ $$

Question Number 154328 Answers: 2 Comments: 0

S=(1/(1+10))+(2/(1+10^2 ))+(4/(1+10^4 ))+(8/(1+10^8 ))+…

$$\:{S}=\frac{\mathrm{1}}{\mathrm{1}+\mathrm{10}}+\frac{\mathrm{2}}{\mathrm{1}+\mathrm{10}^{\mathrm{2}} }+\frac{\mathrm{4}}{\mathrm{1}+\mathrm{10}^{\mathrm{4}} }+\frac{\mathrm{8}}{\mathrm{1}+\mathrm{10}^{\mathrm{8}} }+\ldots\: \\ $$$$ \\ $$

Question Number 154330 Answers: 1 Comments: 0

Question Number 154321 Answers: 2 Comments: 0

Question Number 154316 Answers: 1 Comments: 0

If x^3 + (1/y^3 ) = y^3 + (1/z^3 ) = 1 Find (xyz)^(2025) - 1 = ?

$$\mathrm{If}\:\:\mathrm{x}^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\mathrm{y}^{\mathrm{3}} }\:=\:\mathrm{y}^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{3}} }\:=\:\mathrm{1} \\ $$$$\mathrm{Find}\:\:\left(\mathrm{xyz}\right)^{\mathrm{2025}} \:-\:\mathrm{1}\:=\:? \\ $$

Question Number 154320 Answers: 1 Comments: 0

if a;b;c>0 and ab+bc+ca=2 then: Σ_(cyc) ((a(b^4 + c^4 ))/(b^3 + b^2 c + bc^2 + c^3 )) ≥ 1

$$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{ab}+\mathrm{bc}+\mathrm{ca}=\mathrm{2}\:\:\mathrm{then}: \\ $$$$\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\frac{\mathrm{a}\left(\mathrm{b}^{\mathrm{4}} \:+\:\mathrm{c}^{\mathrm{4}} \right)}{\mathrm{b}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{2}} \mathrm{c}\:+\:\mathrm{bc}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{3}} }\:\geqslant\:\mathrm{1} \\ $$

Question Number 154318 Answers: 1 Comments: 0

Question Number 154309 Answers: 1 Comments: 0

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