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Question Number 155133 Answers: 2 Comments: 0

Σ_(n=0) ^∞ (((−1)^n )/((2n+1)^3 ))=?

$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{3}} }=? \\ $$

Question Number 155132 Answers: 0 Comments: 0

Question Number 155130 Answers: 1 Comments: 0

Question Number 155126 Answers: 0 Comments: 0

∫_0 ^( ∞) e^(− β (2x+b)^(1/a) ) dx

$$\int_{\mathrm{0}} ^{\:\infty} \:{e}^{−\:\beta\:\left(\mathrm{2}{x}+{b}\right)^{\frac{\mathrm{1}}{\boldsymbol{{a}}}} } \:{dx} \\ $$

Question Number 155122 Answers: 0 Comments: 2

Question Number 155120 Answers: 1 Comments: 0

lim_( x →0) ((1/x^( 2) ) − cot^( 2) (x))=?

$$ \\ $$$$\:\:\:{lim}_{\:{x}\:\rightarrow\mathrm{0}} \left(\frac{\mathrm{1}}{{x}^{\:\mathrm{2}} }\:−\:{cot}^{\:\mathrm{2}} \left({x}\right)\right)=? \\ $$$$ \\ $$

Question Number 155153 Answers: 1 Comments: 0

Solve the equation in R (√(2(x^2 - x + 1))) = 1 + (√x) - x

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{in}\:\mathbb{R} \\ $$$$\sqrt{\mathrm{2}\left(\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{x}\:+\:\mathrm{1}\right)}\:=\:\mathrm{1}\:+\:\sqrt{\mathrm{x}}\:-\:\mathrm{x} \\ $$

Question Number 155109 Answers: 1 Comments: 0

how many terms contain “ ab^2 c^3 ” in (a+2b+3c+4d^2 +5e^3 )^(10) ?

$$\mathrm{how}\:\mathrm{many}\:\mathrm{terms}\:\mathrm{contain}\:``\:\mathrm{ab}^{\mathrm{2}} \mathrm{c}^{\mathrm{3}} \:''\:\mathrm{in}\:\left(\mathrm{a}+\mathrm{2b}+\mathrm{3c}+\mathrm{4d}^{\mathrm{2}} +\mathrm{5e}^{\mathrm{3}} \right)^{\mathrm{10}} \:? \\ $$

Question Number 155106 Answers: 1 Comments: 3

Solve for real numbers: { (((√(x+y)) - (√(x-y)) + (√(x^2 -y^2 )) = 5)),((2x + 3(√(x^2 -y^2 )) = 19)) :}

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\begin{cases}{\sqrt{\mathrm{x}+\mathrm{y}}\:-\:\sqrt{\mathrm{x}-\mathrm{y}}\:+\:\sqrt{\mathrm{x}^{\mathrm{2}} -\mathrm{y}^{\mathrm{2}} }\:=\:\mathrm{5}}\\{\mathrm{2x}\:+\:\mathrm{3}\sqrt{\mathrm{x}^{\mathrm{2}} -\mathrm{y}^{\mathrm{2}} }\:=\:\mathrm{19}}\end{cases} \\ $$

Question Number 155101 Answers: 1 Comments: 3

soit: y y′+xy^2 +x=0 ,avec f(0)=1 f′′(0)=?

$${soit}:\:{y}\:{y}'+{xy}^{\mathrm{2}} +{x}=\mathrm{0}\:,{avec}\:{f}\left(\mathrm{0}\right)=\mathrm{1} \\ $$$${f}''\left(\mathrm{0}\right)=? \\ $$

Question Number 155100 Answers: 1 Comments: 2

Determine all triangle with: 1.The lengths of sides positive integers and at least one is prime number. 2.The semiperimetr is positive integer and area is equal with perimetr.

$$\mathrm{Determine}\:\mathrm{all}\:\mathrm{triangle}\:\mathrm{with}: \\ $$$$\mathrm{1}.\mathrm{The}\:\mathrm{lengths}\:\mathrm{of}\:\mathrm{sides}\:\mathrm{positive}\:\mathrm{integers} \\ $$$$\:\:\:\:\:\mathrm{and}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{is}\:\mathrm{prime}\:\mathrm{number}. \\ $$$$\mathrm{2}.\mathrm{The}\:\mathrm{semiperimetr}\:\mathrm{is}\:\mathrm{positive}\:\mathrm{integer} \\ $$$$\:\:\:\:\:\mathrm{and}\:\mathrm{area}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{with}\:\mathrm{perimetr}. \\ $$

Question Number 155083 Answers: 1 Comments: 0

Question Number 155079 Answers: 0 Comments: 1

Question Number 155259 Answers: 1 Comments: 2

If: x+(1/x)=6 then x^3 +(1/x^3 )=?

$${If}:\:{x}+\frac{\mathrm{1}}{{x}}=\mathrm{6}\:\:{then}\:\:{x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}} }=? \\ $$

Question Number 155075 Answers: 1 Comments: 4

Question Number 155069 Answers: 0 Comments: 0

if x;y;z>0 such that x+y+z=3 and 0≤𝛌≤1 then prove that: (x/(y^2 +λ)) + (y/(z^2 +λ)) + (z/(x^2 +λ)) ≥ (3/(λ+1))

$$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:\:\mathrm{such}\:\mathrm{that}\:\:\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{3} \\ $$$$\mathrm{and}\:\:\mathrm{0}\leqslant\boldsymbol{\lambda}\leqslant\mathrm{1}\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{x}}{\mathrm{y}^{\mathrm{2}} +\lambda}\:+\:\frac{\mathrm{y}}{\mathrm{z}^{\mathrm{2}} +\lambda}\:+\:\frac{\mathrm{z}}{\mathrm{x}^{\mathrm{2}} +\lambda}\:\geqslant\:\frac{\mathrm{3}}{\lambda+\mathrm{1}} \\ $$

Question Number 155068 Answers: 0 Comments: 0

Question Number 155257 Answers: 1 Comments: 5

Question Number 155206 Answers: 0 Comments: 0

Determine all positive integers a;b;c;d;x;y;z;t and a≠b≠c≠d which satisfy a+b+c=td ; b+c+d=xa ; c+d+a=yb ; d+a+b=zc

$$\mathrm{Determine}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{integers} \\ $$$$\mathrm{a};\mathrm{b};\mathrm{c};\mathrm{d};\mathrm{x};\mathrm{y};\mathrm{z};\mathrm{t}\:\:\mathrm{and}\:\:\mathrm{a}\neq\mathrm{b}\neq\mathrm{c}\neq\mathrm{d} \\ $$$$\mathrm{which}\:\mathrm{satisfy}\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{td}\:; \\ $$$$\mathrm{b}+\mathrm{c}+\mathrm{d}=\mathrm{xa}\:;\:\mathrm{c}+\mathrm{d}+\mathrm{a}=\mathrm{yb}\:;\:\mathrm{d}+\mathrm{a}+\mathrm{b}=\mathrm{zc} \\ $$

Question Number 155207 Answers: 1 Comments: 0

𝛀 =∫_( 0) ^( ∞) ((ln(x))/(e^x + e^(−x) )) dx = ?

$$\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{e}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{e}^{−\boldsymbol{\mathrm{x}}} }\:\mathrm{dx}\:=\:? \\ $$

Question Number 155058 Answers: 0 Comments: 0

Question Number 155056 Answers: 1 Comments: 0

Question Number 155039 Answers: 2 Comments: 0

(2/5) + (6/5) = ? Hihi

$$\frac{\mathrm{2}}{\mathrm{5}}\:+\:\frac{\mathrm{6}}{\mathrm{5}}\:=\:?\:\:{Hihi} \\ $$

Question Number 155036 Answers: 1 Comments: 0

If a^b =b^a and a=2b then find the value of a^2 +b^2 ?

$$\:\mathrm{If}\:\:\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{b}}} =\boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{a}}} \:\mathrm{and}\:\boldsymbol{\mathrm{a}}=\mathrm{2}\boldsymbol{\mathrm{b}}\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\:\:\mathrm{value}\:\mathrm{of}\:\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{b}}^{\mathrm{2}} \:? \\ $$

Question Number 155035 Answers: 1 Comments: 0

Question Number 155034 Answers: 3 Comments: 4

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