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A=((((x+((2ax^2 ))^(1/3) )(2a+((2a^2 x))^(1/3) )^(−1) −1)/( (x)^(1/3) −((2a))^(1/3) ))−(2a)^(−1/3) )^(−6) , (a,b)∈R^2 a- A=((16a^4 )/x^2 ) b- A=(8/(ax)) c-A=(((2a))^(1/3) /(3x^3 ))

$$\mathrm{A}=\left(\frac{\left(\mathrm{x}+\sqrt[{\mathrm{3}}]{\mathrm{2ax}^{\mathrm{2}} }\right)\left(\mathrm{2a}+\sqrt[{\mathrm{3}}]{\mathrm{2a}^{\mathrm{2}} \mathrm{x}}\right)^{−\mathrm{1}} −\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{x}}−\sqrt[{\mathrm{3}}]{\mathrm{2a}}}−\left(\mathrm{2a}\right)^{−\mathrm{1}/\mathrm{3}} \right)^{−\mathrm{6}} ,\:\left(\mathrm{a},\mathrm{b}\right)\in\mathbb{R}^{\mathrm{2}} \\ $$$$\mathrm{a}-\:\mathrm{A}=\frac{\mathrm{16a}^{\mathrm{4}} }{\mathrm{x}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{b}-\:\mathrm{A}=\frac{\mathrm{8}}{\mathrm{ax}}\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{c}-\mathrm{A}=\frac{\sqrt[{\mathrm{3}}]{\mathrm{2a}}}{\mathrm{3x}^{\mathrm{3}} } \\ $$

Question Number 146761 Answers: 1 Comments: 1

Solve the partial defferintial equation u_t =a^2 u_(xx) ,0<x<L ,t>0 u(0,t)=0 and u(L,t)=0 and u_x (x,0)=f(x)

$${Solve}\:{the}\:{partial}\:{defferintial}\:{equation} \\ $$$${u}_{{t}} ={a}^{\mathrm{2}} {u}_{{xx}} \:\:\:,\mathrm{0}<{x}<{L}\:,{t}>\mathrm{0} \\ $$$$ \\ $$$${u}\left(\mathrm{0},{t}\right)=\mathrm{0}\:\:{and}\:{u}\left({L},{t}\right)=\mathrm{0}\:\:{and}\:{u}_{{x}} \left({x},\mathrm{0}\right)={f}\left({x}\right) \\ $$

Question Number 146758 Answers: 2 Comments: 0

find forier series to half rang of f(x)=sinx ,0<x<π and prove that Σ_(n=1) ^∞ (1/(4n^2 −1))=(1/2)

$${find}\:{forier}\:{series}\:{to}\:{half}\:{rang}\:{of}\: \\ $$$${f}\left({x}\right)={sinx}\:\:,\mathrm{0}<{x}<\pi\:{and}\:{prove}\:{that} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 146756 Answers: 2 Comments: 0

∫_( 0) ^( 1) t^2 + 1 dt

$$ \\ $$$$ \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:{t}^{\mathrm{2}} \:+\:\mathrm{1}\:{dt} \\ $$

Question Number 146755 Answers: 0 Comments: 0

lim_(p→+∞) Σ_(k=1) ^(p−1) (2/(k^2 (p−k)^2 ))=...?

$$\underset{{p}\rightarrow+\infty} {\mathrm{lim}}\:\underset{{k}=\mathrm{1}} {\overset{{p}−\mathrm{1}} {\sum}}\frac{\mathrm{2}}{{k}^{\mathrm{2}} \left({p}−{k}\right)^{\mathrm{2}} }=...? \\ $$

Question Number 146752 Answers: 1 Comments: 0

∫_( 0) ^( 1) t^2 + (1/2)t −6dx

$$ \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:{t}^{\mathrm{2}} +\:\frac{\mathrm{1}}{\mathrm{2}}{t}\:−\mathrm{6}{dx}\:\: \\ $$

Question Number 146746 Answers: 4 Comments: 0

∫_( 0) ^( 4) (√(16 - x^2 )) dx = ?

$$\underset{\:\mathrm{0}} {\overset{\:\mathrm{4}} {\int}}\:\sqrt{\mathrm{16}\:-\:{x}^{\mathrm{2}} }\:{dx}\:=\:? \\ $$

Question Number 146744 Answers: 1 Comments: 0

if ∫_a ^b f(x)dx = 7 and ∫_a ^b 4 g(x)dx = −6 find ∫_a ^b (3 f(x)−8 g(x)) dx = ?

$${if}\:\:\underset{\boldsymbol{{a}}} {\overset{\boldsymbol{{b}}} {\int}}{f}\left({x}\right){dx}\:=\:\mathrm{7}\:\:\:{and}\:\:\underset{\boldsymbol{{a}}} {\overset{\boldsymbol{{b}}} {\int}}\mathrm{4}\:{g}\left({x}\right){dx}\:=\:−\mathrm{6} \\ $$$${find}\:\:\:\underset{\boldsymbol{{a}}} {\overset{\boldsymbol{{b}}} {\int}}\left(\mathrm{3}\:{f}\left({x}\right)−\mathrm{8}\:{g}\left({x}\right)\right)\:{dx}\:=\:? \\ $$

Question Number 146736 Answers: 1 Comments: 0

1: S:= Σ_(n=1) ^∞ (((−1)^( n−1) )/(n.2^( n) )) =? 2: A:= Σ(((−1)^( n−1) )/(n^2 . 2^( n) )) =?

$$ \\ $$$$\:\:\:\:\:\:\mathrm{1}:\:\:\:\:\mathrm{S}:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{\:{n}−\mathrm{1}} }{{n}.\mathrm{2}^{\:{n}} }\:=? \\ $$$$\:\:\:\:\:\:\mathrm{2}:\:\:\:\:\mathrm{A}:=\:\Sigma\frac{\left(−\mathrm{1}\right)^{\:{n}−\mathrm{1}} }{{n}^{\mathrm{2}} .\:\mathrm{2}^{\:{n}} }\:=? \\ $$

Question Number 146735 Answers: 2 Comments: 0

Σ_(n=1) ^∞ ((1+(1/2)+(1/3)+...+(1/n))/((n+1)(n+2)))=?

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

Question Number 146729 Answers: 0 Comments: 0

Question Number 146725 Answers: 2 Comments: 0

cos(x) ∙ cos(3x) = cos(5x) ∙ cos(7x) ⇒ x = ?

$${cos}\left({x}\right)\:\centerdot\:{cos}\left(\mathrm{3}{x}\right)\:=\:{cos}\left(\mathrm{5}{x}\right)\:\centerdot\:{cos}\left(\mathrm{7}{x}\right) \\ $$$$\Rightarrow\:{x}\:=\:? \\ $$

Question Number 146705 Answers: 1 Comments: 0

find lim_(x→0) ((sin(tan(2x)−x)+1−cos(πx^2 ))/x^2 )

$$\mathrm{find}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\frac{\mathrm{sin}\left(\mathrm{tan}\left(\mathrm{2x}\right)−\mathrm{x}\right)+\mathrm{1}−\mathrm{cos}\left(\pi\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{2}} } \\ $$

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