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Question Number 163759 Answers: 3 Comments: 0

∫_0 ^1 (((ln(1+x))/x))^2 dx=? by M.A

$$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\frac{\boldsymbol{\mathrm{ln}}\left(\mathrm{1}+\boldsymbol{\mathrm{x}}\right)}{\boldsymbol{\mathrm{x}}}\right)^{\mathrm{2}} \boldsymbol{\mathrm{dx}}=? \\ $$$$\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{M}}.\boldsymbol{\mathrm{A}} \\ $$

Question Number 163751 Answers: 1 Comments: 0

∫_0 ^1 ln(1+x)ln(1−x)dx=? by MATH.AMIN −−−−−−−−−−−−−−−−−−−−

$$\int_{\mathrm{0}} ^{\mathrm{1}} \boldsymbol{{ln}}\left(\mathrm{1}+\boldsymbol{{x}}\right)\boldsymbol{{ln}}\left(\mathrm{1}−\boldsymbol{{x}}\right)\boldsymbol{{dx}}=? \\ $$$$\boldsymbol{{by}}\:\boldsymbol{{MATH}}.\boldsymbol{{AMIN}} \\ $$$$−−−−−−−−−−−−−−−−−−−− \\ $$

Question Number 163747 Answers: 2 Comments: 0

a^2 (a - 3b) = b^2 (b - 3a) + 27 ab = 2 find a^3 - b^3 = ?

$$\mathrm{a}^{\mathrm{2}} \left(\mathrm{a}\:-\:\mathrm{3b}\right)\:=\:\mathrm{b}^{\mathrm{2}} \left(\mathrm{b}\:-\:\mathrm{3a}\right)\:+\:\mathrm{27} \\ $$$$\mathrm{ab}\:=\:\mathrm{2} \\ $$$$\mathrm{find}\:\:\mathrm{a}^{\mathrm{3}} \:-\:\mathrm{b}^{\mathrm{3}} \:=\:? \\ $$

Question Number 163746 Answers: 3 Comments: 0

x^2 + 5y^2 - 4xy + 6y + 9 = 0 find xy=?

$$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{5y}^{\mathrm{2}} \:-\:\mathrm{4xy}\:+\:\mathrm{6y}\:+\:\mathrm{9}\:=\:\mathrm{0} \\ $$$$\mathrm{find}\:\:\mathrm{xy}=? \\ $$

Question Number 163743 Answers: 0 Comments: 0

Question Number 163741 Answers: 0 Comments: 4

Question Number 163736 Answers: 1 Comments: 0

Question Number 163735 Answers: 0 Comments: 1

Question Number 163733 Answers: 0 Comments: 0

prove v=(√((F∙L)/m)) ?

$${prove}\:{v}=\sqrt{\frac{{F}\centerdot{L}}{{m}}}\:\:\:? \\ $$

Question Number 163732 Answers: 0 Comments: 0

If , 𝛗 = ∫_(−∞) ^( +∞) (( sin(x).ln^( 2) (x ))/x) then find : Im (𝛗 ) = ? ■ m.n

$$ \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\mathrm{I}{f}\:,\:\:\boldsymbol{\phi}\:=\:\int_{−\infty} ^{\:+\infty} \frac{\:{sin}\left({x}\right).{ln}^{\:\mathrm{2}} \left({x}\:\right)}{{x}}\:\:{then} \\ $$$$\:\:\:\:\:\:{find}\:\::\:\:\:\:\:\:\:\:\:\mathcal{I}{m}\:\left(\boldsymbol{\phi}\:\right)\:=\:?\:\:\:\:\:\:\:\:\:\:\blacksquare\:{m}.{n}\: \\ $$$$ \\ $$

Question Number 163730 Answers: 2 Comments: 0

Find: 𝛀 = ∫ ((sin(x) + (√3) cos(x))/(sin(3x))) dx

$$\mathrm{Find}:\:\:\boldsymbol{\Omega}\:=\:\int\:\frac{\mathrm{sin}\left(\mathrm{x}\right)\:+\:\sqrt{\mathrm{3}}\:\mathrm{cos}\left(\mathrm{x}\right)}{\mathrm{sin}\left(\mathrm{3x}\right)}\:\mathrm{dx} \\ $$

Question Number 163720 Answers: 1 Comments: 0

∫_2 ^( 4) ((√(ln(9−x)))/( (√(ln(9−x)))+(√(ln(3+x))))) dx

$$\int_{\mathrm{2}} ^{\:\mathrm{4}} \frac{\sqrt{{ln}\left(\mathrm{9}−{x}\right)}}{\:\sqrt{{ln}\left(\mathrm{9}−{x}\right)}+\sqrt{{ln}\left(\mathrm{3}+{x}\right)}}\:{dx} \\ $$$$ \\ $$

Question Number 163719 Answers: 1 Comments: 0

Evaluate the following limit: Φ =lim_(n→∞) - (1/(n!)) ∙ (d^n /dx^n ) ((e^(x-1) /(x - 1)))∣_(x=0)

$$\mathrm{Evaluate}\:\mathrm{the}\:\mathrm{following}\:\mathrm{limit}: \\ $$$$\Phi\:=\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:-\:\frac{\mathrm{1}}{\mathrm{n}!}\:\centerdot\:\frac{\mathrm{d}^{\boldsymbol{\mathrm{n}}} }{\mathrm{dx}^{\boldsymbol{\mathrm{n}}} }\:\left(\frac{\mathrm{e}^{\boldsymbol{\mathrm{x}}-\mathrm{1}} }{\mathrm{x}\:-\:\mathrm{1}}\right)\mid_{\boldsymbol{\mathrm{x}}=\mathrm{0}} \\ $$

Question Number 163718 Answers: 0 Comments: 0

let m∈N and 0<x<m if i = [(((m + 1)x)/(x + 1))] prove that 2 ((m),(( i)) ) ≥ x^(m-i) where [x] is integer part of x and ((m),(( i)) ) is a binomial coefficient

$$\mathrm{let}\:\:\mathrm{m}\in\mathbb{N}\:\:\mathrm{and}\:\:\mathrm{0}<\mathrm{x}<\mathrm{m} \\ $$$$\mathrm{if}\:\:\:\boldsymbol{\mathrm{i}}\:=\:\left[\frac{\left(\mathrm{m}\:+\:\mathrm{1}\right)\mathrm{x}}{\mathrm{x}\:+\:\mathrm{1}}\right] \\ $$$$\mathrm{prove}\:\mathrm{that}\:\:\:\mathrm{2}\begin{pmatrix}{\mathrm{m}}\\{\:\:\mathrm{i}}\end{pmatrix}\:\geqslant\:\mathrm{x}^{\boldsymbol{\mathrm{m}}-\boldsymbol{\mathrm{i}}} \\ $$$$\mathrm{where}\:\left[\boldsymbol{\mathrm{x}}\right]\:\mathrm{is}\:\mathrm{integer}\:\mathrm{part}\:\mathrm{of}\:\boldsymbol{\mathrm{x}}\:\mathrm{and}\:\begin{pmatrix}{\mathrm{m}}\\{\:\:\mathrm{i}}\end{pmatrix} \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{binomial}\:\mathrm{coefficient} \\ $$

Question Number 163715 Answers: 0 Comments: 0

Question Number 163709 Answers: 1 Comments: 0

CALCULUS ∫_0 ^1 (x^(2n−1) /(x+1))dx=? n≥1

$$\boldsymbol{\mathrm{CALCULUS}} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}\boldsymbol{\mathrm{n}}−\mathrm{1}} }{\boldsymbol{\mathrm{x}}+\mathrm{1}}\boldsymbol{\mathrm{dx}}=?\:\:\:\:\:\boldsymbol{\mathrm{n}}\geqslant\mathrm{1} \\ $$

Question Number 163707 Answers: 0 Comments: 0

etudier suivant les reels a et b la convergence Σ_(n=1) (a^n /(b^n +n))

$${etudier}\:{suivant}\:{les}\:{reels}\:\:{a}\:{et}\:{b}\:{la}\:{convergence} \\ $$$$\underset{{n}=\mathrm{1}} {\sum}\frac{{a}^{{n}} }{{b}^{{n}} +{n}} \\ $$

Question Number 163704 Answers: 2 Comments: 0

Ω= Σ_(n=1) ^∞ n(ζ (1+n) −1) =?

$$ \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\Omega=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{n}\left(\zeta\:\left(\mathrm{1}+{n}\right)\:−\mathrm{1}\right)\:=? \\ $$$$ \\ $$

Question Number 163700 Answers: 3 Comments: 0

K(x) = ((3 cos x)/(5+4sin x)) {: ((max K(x))),((min K(x))) } =?

$$\:\:\mathcal{K}\left({x}\right)\:=\:\frac{\mathrm{3}\:\mathrm{cos}\:{x}}{\mathrm{5}+\mathrm{4sin}\:{x}} \\ $$$$\:\left.\begin{matrix}{{max}\:\mathcal{K}\left({x}\right)}\\{{min}\:\mathcal{K}\left({x}\right)}\end{matrix}\right\}\:=? \\ $$

Question Number 163692 Answers: 1 Comments: 0

A 10 liter bottle filled with a 20% alcohol solution. How much 75% alcohol solution should be added to obtain 45% alcohol solution? a) 1.62 lit b) 1.72 lit. c) 1.82 lit d) 1.92 lit.

$$ \\ $$A 10 liter bottle filled with a 20% alcohol solution. How much 75% alcohol solution should be added to obtain 45% alcohol solution? a) 1.62 lit b) 1.72 lit. c) 1.82 lit d) 1.92 lit.

Question Number 163690 Answers: 1 Comments: 0

lim_(x→0) ((cos 2x cos 4x cos 8x − 3x csc 2x)/(2x^2 )) =?

$$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{2}{x}\:\mathrm{cos}\:\mathrm{4}{x}\:\mathrm{cos}\:\mathrm{8}{x}\:−\:\mathrm{3}{x}\:\mathrm{csc}\:\mathrm{2}{x}}{\mathrm{2}{x}^{\mathrm{2}} }\:=? \\ $$

Question Number 163688 Answers: 2 Comments: 0

Question Number 163687 Answers: 0 Comments: 0

Question Number 163682 Answers: 1 Comments: 0

Ω= ∫_0 ^( 1) (Li_( 2) ^ (x ))^( 2) dx = ? ■ m.n −−− −−−

$$ \\ $$$$\:\:\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\left(\mathrm{Li}_{\:\mathrm{2}} ^{\:} \left({x}\:\right)\right)^{\:\mathrm{2}} {dx}\:=\:?\:\:\:\:\:\:\blacksquare\:{m}.{n}\:\:\: \\ $$$$\:\:\:\:\:−−−\:−−− \\ $$$$\:\:\:\: \\ $$

Question Number 163675 Answers: 0 Comments: 1

how do we find the sum of the terms after the n^(th) term of a GP

$${how}\:{do}\:{we}\:{find}\:{the}\:{sum}\:{of}\:{the}\:{terms}\:{after}\: \\ $$$${the}\:{n}^{{th}} \:{term}\:{of}\:{a}\:{GP} \\ $$

Question Number 163666 Answers: 4 Comments: 0

lim _(x→𝛑) (((x^𝛑 − 𝛑^x )/(x−𝛑))) =?? ≪zaynal≫

$$\boldsymbol{\mathrm{lim}}\:_{\boldsymbol{{x}}\rightarrow\boldsymbol{\pi}} \:\:\left(\frac{\boldsymbol{{x}}^{\boldsymbol{\pi}} \:−\:\boldsymbol{\pi}^{\boldsymbol{{x}}} }{\boldsymbol{{x}}−\boldsymbol{\pi}}\right)\:=?? \\ $$$$\ll\mathrm{zaynal}\gg \\ $$

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