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Question Number 163735    Answers: 0   Comments: 1

Question Number 163733    Answers: 0   Comments: 0

prove v=(√((Fβˆ™L)/m)) ?

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

Question Number 163732    Answers: 0   Comments: 0

If , 𝛗 = ∫_(βˆ’βˆž) ^( +∞) (( sin(x).ln^( 2) (x ))/x) then find : Im (𝛗 ) = ? β–  m.n

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

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(9βˆ’x)))/( (√(ln(9βˆ’x)))+(√(ln(3+x))))) dx

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

Question Number 163719    Answers: 1   Comments: 0

Evaluate the following limit: Ξ¦ =lim_(nβ†’βˆž) - (1/(n!)) βˆ™ (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)) ) β‰₯ 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^(2nβˆ’1) /(x+1))dx=? nβ‰₯1

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

Question Number 163707    Answers: 0   Comments: 0

etudier suivant les reels a et b la convergence Ξ£_(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

Ξ©= Ξ£_(n=1) ^∞ n(ΞΆ (1+n) βˆ’1) =?

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

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_(xβ†’0) ((cos 2x cos 4x cos 8x βˆ’ 3x csc 2x)/(2x^2 )) =?

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

Question Number 163688    Answers: 2   Comments: 0

Question Number 163687    Answers: 0   Comments: 0

Question Number 163682    Answers: 1   Comments: 0

Ξ©= ∫_0 ^( 1) (Li_( 2) ^ (x ))^( 2) dx = ? β–  m.n βˆ’βˆ’βˆ’ βˆ’βˆ’βˆ’

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

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 βˆ’ 𝛑^x )/(xβˆ’π›‘))) =?? β‰ͺzaynal≫

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

Question Number 163662    Answers: 1   Comments: 1

Question Number 163651    Answers: 1   Comments: 1

if (aβˆ’2b)^2 +(bβˆ’2c)^2 =0 find volve (((b+cβˆ’a)^3 )/(abc))=?

$${if}\:\:\left({a}βˆ’\mathrm{2}{b}\right)^{\mathrm{2}} +\left({b}βˆ’\mathrm{2}{c}\right)^{\mathrm{2}} =\mathrm{0} \\ $$$${find}\:\:{volve}\:\:\frac{\left({b}+{c}βˆ’{a}\right)^{\mathrm{3}} }{{abc}}=? \\ $$

Question Number 163650    Answers: 1   Comments: 2

lim_(xβ†’Ο€) ((x^Ο€^x βˆ’Ο€^x^Ο€ )/(xβˆ’Ο€))=?

$$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\frac{{x}^{\pi^{{x}} } βˆ’\pi^{{x}^{\pi} } }{{x}βˆ’\pi}=? \\ $$

Question Number 163642    Answers: 1   Comments: 0

lim_(xβ†’(2/3)) ((⌊3xβŒ‹βˆ’3x)/(9x^2 βˆ’4)) =?

$$\:\:\:\:\:\:\underset{{x}\rightarrow\frac{\mathrm{2}}{\mathrm{3}}} {\mathrm{lim}}\:\frac{\lfloor\mathrm{3}{x}\rfloorβˆ’\mathrm{3}{x}}{\mathrm{9}{x}^{\mathrm{2}} βˆ’\mathrm{4}}\:=? \\ $$

Question Number 163638    Answers: 0   Comments: 2

∫ (dx/( (√(2c_1 +e^(βˆ’2x) ))))

$$\int\:\frac{\boldsymbol{{dx}}}{\:\sqrt{\mathrm{2}\boldsymbol{{c}}_{\mathrm{1}} +\boldsymbol{{e}}^{βˆ’\mathrm{2}\boldsymbol{{x}}} }} \\ $$

Question Number 163632    Answers: 2   Comments: 0

(((x^2 - y^2 )βˆ™(√3))/( (√(x^3 + 3x^2 y + 3xy^2 + y^3 )))) = -1 x^3 + y^3 = (x + y)^2 find: x and y

$$\frac{\left(\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{y}^{\mathrm{2}} \right)\centerdot\sqrt{\mathrm{3}}}{\:\sqrt{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{3x}^{\mathrm{2}} \mathrm{y}\:+\:\mathrm{3xy}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{3}} }}\:=\:-\mathrm{1} \\ $$$$\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:=\:\left(\mathrm{x}\:+\:\mathrm{y}\right)^{\mathrm{2}} \\ $$$$\mathrm{find}:\:\:\boldsymbol{\mathrm{x}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{y}} \\ $$

Question Number 163631    Answers: 2   Comments: 0

x + (1/x) = (√3) β‡’ x^(3579) + (1/x^(3579) ) = ?

$$\mathrm{x}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\:=\:\sqrt{\mathrm{3}}\:\:\Rightarrow\:\mathrm{x}^{\mathrm{3579}} \:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3579}} }\:=\:? \\ $$

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