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Question Number 143576    Answers: 0   Comments: 0

find L(((arctanx)/x))

$${find}\:{L}\left(\frac{{arctanx}}{{x}}\right) \\ $$

Question Number 143575    Answers: 1   Comments: 0

find L(e^(−(√x)) )

$${find}\:{L}\left({e}^{−\sqrt{{x}}} \right) \\ $$

Question Number 143570    Answers: 1   Comments: 0

Question Number 143715    Answers: 0   Comments: 0

∫_0 ^(π/4) tanx∙Li(tan^2 x)dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \mathrm{tanx}\centerdot\mathrm{Li}\left(\mathrm{tan}^{\mathrm{2}} \mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 143562    Answers: 0   Comments: 0

Question Number 143561    Answers: 3   Comments: 0

lim_(x→∞) (1−(2/x^ )+(1/x^2 ))^x =? lim_(n→∞) ((√n)−(√(n−1)))(√(n+1)) =?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{1}−\frac{\mathrm{2}}{{x}^{} }+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)^{{x}} =? \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\sqrt{{n}}−\sqrt{{n}−\mathrm{1}}\right)\sqrt{{n}+\mathrm{1}}\:=? \\ $$

Question Number 143556    Answers: 0   Comments: 0

∫_0 ^∞ (dx/(x^α (lnx)^β ))

$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{dx}}{\mathrm{x}^{\alpha} \left(\mathrm{lnx}\right)^{\beta} } \\ $$

Question Number 143546    Answers: 1   Comments: 0

calculate ∫_0 ^∞ ((log^2 x)/((8+x^4 )^2 ))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{log}^{\mathrm{2}} \mathrm{x}}{\left(\mathrm{8}+\mathrm{x}^{\mathrm{4}} \right)^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 143542    Answers: 0   Comments: 0

calculate the polar integral that give the area of the region bunded by the curves r=2 ,r=4cosθ and ,r cosθ=3

$${calculate}\:{the}\:{polar}\:{integral}\:{that} \\ $$$$\:{give}\:{the}\:{area}\:{of}\:{the}\:{region}\:{bunded}\:{by}\:{the}\:{curves}\: \\ $$$$ \\ $$$${r}=\mathrm{2}\:,{r}=\mathrm{4}{cos}\theta\:{and}\:,{r}\:{cos}\theta=\mathrm{3}\: \\ $$$$ \\ $$

Question Number 143531    Answers: 1   Comments: 0

lim_(x→+∞) ((2(√x)+3 (x)^(1/3) +5 (x)^(1/5) )/( (√(3x−2)) +((2x−3))^(1/3) )) =?

$$\:\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:\frac{\mathrm{2}\sqrt{{x}}+\mathrm{3}\:\sqrt[{\mathrm{3}}]{{x}}\:+\mathrm{5}\:\sqrt[{\mathrm{5}}]{{x}}}{\:\sqrt{\mathrm{3}{x}−\mathrm{2}}\:+\sqrt[{\mathrm{3}}]{\mathrm{2}{x}−\mathrm{3}}}\:=? \\ $$

Question Number 143532    Answers: 1   Comments: 0

lim_(x→0) ((1−(√(1+x^2 )) cos x)/(tan^4 x)) =?

$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:\mathrm{cos}\:{x}}{\mathrm{tan}\:^{\mathrm{4}} {x}}\:=? \\ $$

Question Number 143523    Answers: 1   Comments: 0

Determiner l′origine de laplace 1−F(p)=(p/((p+2)^2 ))

$${Determiner}\:{l}'{origine}\:{de}\:{laplace} \\ $$$$\mathrm{1}−{F}\left({p}\right)=\frac{{p}}{\left({p}+\mathrm{2}\right)^{\mathrm{2}} } \\ $$

Question Number 143521    Answers: 0   Comments: 1

Question Number 143519    Answers: 3   Comments: 0

The first two terms of the {a_n } series are defind as a_n =a_(n−1) +a_(n−2) for the general term a_1 =5, a_2 =8 and n≥3 . since the L=lim_(n→∞) (a_(n+1) /a_n ) what is the value of L

$$ \\ $$$${The}\:{first}\:{two}\:{terms}\:{of}\:{the}\:\left\{{a}_{{n}} \right\}\:{series}\:\:\:{are}\:{defind}\:{as}\:{a}_{{n}} ={a}_{{n}−\mathrm{1}} +{a}_{{n}−\mathrm{2}} \:\:{for}\:{the}\:{general}\:{term} \\ $$$$\:{a}_{\mathrm{1}} =\mathrm{5},\:{a}_{\mathrm{2}} =\mathrm{8}\:{and}\:{n}\geqslant\mathrm{3}\:. \\ $$$${since}\:{the}\:{L}={li}\underset{{n}\rightarrow\infty} {{m}}\frac{{a}_{{n}+\mathrm{1}} }{{a}_{{n}} }\:\:{what}\:{is}\:{the}\:{value}\:{of}\:{L} \\ $$$$ \\ $$

Question Number 143516    Answers: 2   Comments: 1

Question Number 143508    Answers: 3   Comments: 0

..........Calculus........ i: 𝛗_1 :=∫_0 ^( 1) ((ln^2 (1−x).ln(x))/x)dx ii: 𝛗_2 := ∫_0 ^( 1) ((ln^2 (x).ln(1−x))/x) dx iii : 𝛗_3 :=∫_0 ^( 1) ((ln^2 (x).ln(1+x))/x)dx

$$ \\ $$$$\:\:\:\:\:\:\:\:..........{Calculus}........ \\ $$$$\:\:\:\:{i}:\:\:\:\boldsymbol{\phi}_{\mathrm{1}} :=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} \left(\mathrm{1}−{x}\right).{ln}\left({x}\right)}{{x}}{dx} \\ $$$$\:\:\:{ii}:\:\:\:\boldsymbol{\phi}_{\mathrm{2}} :=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} \left({x}\right).{ln}\left(\mathrm{1}−{x}\right)}{{x}}\:{dx} \\ $$$$\:\:{iii}\::\:\boldsymbol{\phi}_{\mathrm{3}} \::=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} \left({x}\right).{ln}\left(\mathrm{1}+{x}\right)}{{x}}{dx} \\ $$

Question Number 143507    Answers: 1   Comments: 0

10(√(20))+13(√(45))

$$\mathrm{10}\sqrt{\mathrm{20}}+\mathrm{13}\sqrt{\mathrm{45}} \\ $$

Question Number 143506    Answers: 1   Comments: 0

∫_1 ^∞ (1/(e^(−x) +e^x )) dx=?

$$\underset{\mathrm{1}} {\overset{\infty} {\int}}\frac{\mathrm{1}}{{e}^{−{x}} +{e}^{{x}} }\:{dx}=? \\ $$$$ \\ $$

Question Number 143505    Answers: 1   Comments: 1

Question Number 143501    Answers: 0   Comments: 0

Question Number 143502    Answers: 0   Comments: 0

Question Number 143499    Answers: 1   Comments: 1

Question Number 143514    Answers: 0   Comments: 1

Question Number 143495    Answers: 1   Comments: 0

On definit la fonction L(f(t))(p)=∫_0 ^(+∞) f(t)e^(−pt) dt Calculer L(((t^n /(n!))))(p)

$${On}\:{definit}\:{la}\:{fonction}\: \\ $$$$\mathscr{L}\left({f}\left({t}\right)\right)\left({p}\right)=\int_{\mathrm{0}} ^{+\infty} {f}\left({t}\right){e}^{−{pt}} {dt} \\ $$$${Calculer}\:\mathscr{L}\left(\left(\frac{{t}^{{n}} }{{n}!}\right)\right)\left({p}\right) \\ $$

Question Number 143493    Answers: 0   Comments: 1

Question Number 143491    Answers: 0   Comments: 1

Find lim_(n→+∝) (u_n ),If { ((u_0 =1,n=1,2,3,.....)),((u_n = ((2018)/(2019))u_(n−1) + (1/((u_(n−1) )^(2018) )))) :}

$$\mathrm{Find}\:\underset{\mathrm{n}\rightarrow+\propto} {\mathrm{lim}}\left(\mathrm{u}_{\mathrm{n}} \right),\mathrm{If}\:\begin{cases}{\mathrm{u}_{\mathrm{0}} =\mathrm{1},\mathrm{n}=\mathrm{1},\mathrm{2},\mathrm{3},.....}\\{\mathrm{u}_{\mathrm{n}} =\:\frac{\mathrm{2018}}{\mathrm{2019}}\mathrm{u}_{\mathrm{n}−\mathrm{1}} +\:\frac{\mathrm{1}}{\left(\mathrm{u}_{\mathrm{n}−\mathrm{1}} \right)^{\mathrm{2018}} }}\end{cases} \\ $$

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