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AllQuestion and Answers: Page 751

Question Number 143808    Answers: 2   Comments: 0

Question Number 143769    Answers: 3   Comments: 0

Question Number 143766    Answers: 1   Comments: 1

x×y′′−y=x^ 3

$${x}×{y}''−{y}=\hat {{x}}\mathrm{3} \\ $$

Question Number 143765    Answers: 1   Comments: 0

∫∫x+2dx

$$\int\int{x}+\mathrm{2}{dx} \\ $$

Question Number 143764    Answers: 1   Comments: 0

can anyone tell me,how can I bring everything in this app to the new phone. And after bringing it to the new phone, I will be able to edit everything again.

$${can}\:{anyone}\:{tell}\:{me},{how}\:{can}\:{I} \\ $$$${bring}\:{everything}\:{in}\:{this}\:{app}\:{to} \\ $$$${the}\:{new}\:{phone}. \\ $$$${And}\:{after}\:{bringing}\:{it}\:{to}\:{the}\:{new} \\ $$$${phone},\:{I}\:{will}\:{be}\:{able}\:{to}\:{edit}\:{everything} \\ $$$${again}. \\ $$

Question Number 143763    Answers: 0   Comments: 0

$$ \: \: \: \: \: \: \: \\ $$$$ \: \: \: \: \: \: \: \: \\ $$$$ \: \: \: \: \: \: \: \: \: \\ $$$$ \: \: \\ $$

Question Number 143758    Answers: 0   Comments: 1

Question Number 143755    Answers: 1   Comments: 0

Study the convergence with respect to α and β the improper integral below; ∫_0 ^∞ (dx/(x^α (lnx)^β ))

$$\mathrm{Study}\:\mathrm{the}\:\mathrm{convergence}\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to} \\ $$$$\alpha\:\mathrm{and}\:\beta\:\mathrm{the}\:\mathrm{improper}\:\mathrm{integral}\:\mathrm{below}; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{dx}}{\mathrm{x}^{\alpha} \left(\mathrm{lnx}\right)^{\beta} } \\ $$

Question Number 143751    Answers: 1   Comments: 0

Question Number 143740    Answers: 1   Comments: 0

Prove that lim_(n→+∞) 2n−(2n+1)ln(n)+Σ_(p=0) ^n ln(1+p^2 )= ln(e^π −e^(−π) )

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}2n}−\left(\mathrm{2n}+\mathrm{1}\right)\mathrm{ln}\left(\mathrm{n}\right)+\underset{\mathrm{p}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\mathrm{ln}\left(\mathrm{1}+\mathrm{p}^{\mathrm{2}} \right)=\:\mathrm{ln}\left({e}^{\pi} −{e}^{−\pi} \right) \\ $$

Question Number 143735    Answers: 1   Comments: 0

.....Calculus..... Ω:= ∫_(−∞) ^( ∞) (dx/(x^( 2) e^(a/x^2 ) )) =? (a > 0 )

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.....{Calculus}..... \\ $$$$\:\:\:\:\:\:\:\:\Omega:=\:\int_{−\infty} ^{\:\infty} \frac{{dx}}{{x}^{\:\mathrm{2}} \:{e}^{\frac{{a}}{{x}^{\mathrm{2}} }} }\:=?\:\:\left({a}\:>\:\mathrm{0}\:\right) \\ $$

Question Number 143731    Answers: 1   Comments: 0

Question Number 143730    Answers: 2   Comments: 0

find lim_(x→0) ((sin(sin(1−cosx))−1+cos(x−sinx))/x^3 )

$$\mathrm{find}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\:\frac{\mathrm{sin}\left(\mathrm{sin}\left(\mathrm{1}−\mathrm{cosx}\right)\right)−\mathrm{1}+\mathrm{cos}\left(\mathrm{x}−\mathrm{sinx}\right)}{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 143728    Answers: 1   Comments: 0

∫_1 ^∞ (({x})/x^3 )dx=1−(π^2 /(12))

$$\int_{\mathrm{1}} ^{\infty} \frac{\left\{{x}\right\}}{{x}^{\mathrm{3}} }{dx}=\mathrm{1}−\frac{\pi^{\mathrm{2}} }{\mathrm{12}} \\ $$

Question Number 143726    Answers: 1   Comments: 2

Question Number 143718    Answers: 0   Comments: 5

Question Number 143709    Answers: 1   Comments: 2

Question Number 143708    Answers: 3   Comments: 0

Prove that (3/4^ )+(3^2 /4^2 )+(3^3 /4^3 )+(3^4 /4^4 )+(3^5 /4^5 )+…=3

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{3}}{\mathrm{4}^{} }+\frac{\mathrm{3}^{\mathrm{2}} }{\mathrm{4}^{\mathrm{2}} }+\frac{\mathrm{3}^{\mathrm{3}} }{\mathrm{4}^{\mathrm{3}} }+\frac{\mathrm{3}^{\mathrm{4}} }{\mathrm{4}^{\mathrm{4}} }+\frac{\mathrm{3}^{\mathrm{5}} }{\mathrm{4}^{\mathrm{5}} }+\ldots=\mathrm{3} \\ $$

Question Number 143706    Answers: 1   Comments: 0

2^x +9^y =x^2 +9xy+y^2 Find x,y∈N

$$\mathrm{2}^{\mathrm{x}} +\mathrm{9}^{\mathrm{y}} =\mathrm{x}^{\mathrm{2}} +\mathrm{9xy}+\mathrm{y}^{\mathrm{2}} \\ $$$$\mathrm{Find}\:\mathrm{x},\mathrm{y}\in\mathbb{N} \\ $$

Question Number 143702    Answers: 2   Comments: 0

n ∈ IN. I_n = ∫_1 ^( e) x^(n+1) lnx dx. 1. prove that (I_n ) is positive and increasing. 2. using a part−by−part integration, calculate I_n .

$${n}\:\in\:\mathrm{IN}. \\ $$$${I}_{{n}} \:=\:\int_{\mathrm{1}} ^{\:\mathrm{e}} {x}^{{n}+\mathrm{1}} {lnx}\:{dx}. \\ $$$$\mathrm{1}.\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\:\left(\boldsymbol{{I}}_{\boldsymbol{{n}}} \right)\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{positive}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{increasing}}. \\ $$$$\mathrm{2}.\:\boldsymbol{\mathrm{using}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{part}}−\boldsymbol{\mathrm{by}}−\boldsymbol{\mathrm{part}}\:\boldsymbol{\mathrm{integration}},\:\boldsymbol{\mathrm{calculate}}\:\boldsymbol{{I}}_{\boldsymbol{{n}}} . \\ $$

Question Number 143701    Answers: 1   Comments: 1

Question Number 143698    Answers: 0   Comments: 5

My first Contribution to this forum. One year later Q 98831

$$\:{My}\:{first}\:{Contribution}\:{to}\:{this}\:{forum}.\: \\ $$$${One}\:{year}\:{later}\: \\ $$$${Q}\:\mathrm{98831} \\ $$

Question Number 143688    Answers: 0   Comments: 2

Question Number 143684    Answers: 1   Comments: 0

x^3 +x−1=^3 (√(2x^3 +11))+(√(5x^2 +16)) Find x∈R

$$\mathrm{x}^{\mathrm{3}} +\mathrm{x}−\mathrm{1}=^{\mathrm{3}} \sqrt{\mathrm{2x}^{\mathrm{3}} +\mathrm{11}}+\sqrt{\mathrm{5x}^{\mathrm{2}} +\mathrm{16}} \\ $$$$\mathrm{Find}\:\mathrm{x}\in\mathbb{R} \\ $$

Question Number 143680    Answers: 1   Comments: 1

tan 76=4 sin^2 14=?

$$\mathrm{tan}\:\mathrm{76}=\mathrm{4} \\ $$$$\mathrm{sin}\:^{\mathrm{2}} \mathrm{14}=? \\ $$

Question Number 143677    Answers: 3   Comments: 0

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