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Question Number 171096    Answers: 1   Comments: 0

∫((x e^(2x) )/((2x+1)^2 ))dx please help

$$ \\ $$$$\int\frac{{x}\:{e}^{\mathrm{2}{x}} }{\left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx}\:\:\:\:{please}\:{help} \\ $$

Question Number 171094    Answers: 0   Comments: 0

prove that: 𝛀=Ξ£_(n=0) ^∞ ((((n!)^2 )/((2n)!)))^2 (2^(4n) /((2n+1)^3 ))=^? (7/2)𝛇(3)βˆ’Ο€G Gβˆ’Catalanβ€²s constant

$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}: \\ $$$$\boldsymbol{\Omega}=\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\left(\boldsymbol{\mathrm{n}}!\right)^{\mathrm{2}} }{\left(\mathrm{2}\boldsymbol{\mathrm{n}}\right)!}\right)^{\mathrm{2}} \frac{\mathrm{2}^{\mathrm{4}\boldsymbol{\mathrm{n}}} }{\left(\mathrm{2}\boldsymbol{\mathrm{n}}+\mathrm{1}\right)^{\mathrm{3}} }\overset{?} {=}\frac{\mathrm{7}}{\mathrm{2}}\boldsymbol{\zeta}\left(\mathrm{3}\right)βˆ’\pi\boldsymbol{\mathrm{G}} \\ $$$$\boldsymbol{\mathrm{G}}βˆ’\boldsymbol{\mathrm{Catalan}}'\boldsymbol{\mathrm{s}}\:\:\boldsymbol{\mathrm{constant}} \\ $$

Question Number 171091    Answers: 0   Comments: 2

Question Number 171090    Answers: 1   Comments: 3

I_n =∫_0 ^1 (1βˆ’u)(√(ud(u))) Demonstrate that βˆ€n∈N, I_(n+1) βˆ’I_n =(1βˆ’u)^n u^(3/2) d(u) and deduce the meaning of variations of (I_n )∈N

$${I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}βˆ’{u}\right)\sqrt{{ud}\left({u}\right)} \\ $$$${Demonstrate}\:{that}\:\forall{n}\in{N},\:{I}_{{n}+\mathrm{1}} βˆ’{I}_{{n}} =\left(\mathrm{1}βˆ’{u}\right)^{{n}} {u}^{\frac{\mathrm{3}}{\mathrm{2}}} {d}\left({u}\right)\:\:{and}\:{deduce}\:{the}\:{meaning}\:{of}\:{variations}\:{of}\:\left({I}_{{n}} \right)\in{N} \\ $$

Question Number 171085    Answers: 1   Comments: 0

43 devided by x remainder is xβˆ’5 how many value of x?

$$\mathrm{43}\:{devided}\:{by}\:{x}\:{remainder}\:{is}\:{x}βˆ’\mathrm{5}\:{how}\:{many}\:{value}\:{of}\:{x}? \\ $$

Question Number 171079    Answers: 1   Comments: 2

lim_(xβ†’0) (((√(1+(√(1+(√(1βˆ’x))))))βˆ’(√(1+(√(1+(√(1+x)))))))/x)=?

$$\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}βˆ’{x}}}}βˆ’\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+{x}}}}}{{x}}=? \\ $$

Question Number 171078    Answers: 1   Comments: 0

sketch the graph of y=ln(x+5)

$$\boldsymbol{\mathrm{sketch}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{graph}}\:\boldsymbol{\mathrm{of}} \\ $$$$\:\boldsymbol{\mathrm{y}}=\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}+\mathrm{5}\right) \\ $$$$ \\ $$

Question Number 171071    Answers: 1   Comments: 0

justify that ∫_0 ^(+∞) (dt/(1+t^4 )) is convergent.

$${justify}\:{that}\:\int_{\mathrm{0}} ^{+\infty} \frac{{dt}}{\mathrm{1}+{t}^{\mathrm{4}} }\:{is}\:{convergent}. \\ $$

Question Number 171070    Answers: 1   Comments: 0

x^2 βˆ’1=2^x find x

$$\boldsymbol{\mathrm{x}}^{\mathrm{2}} βˆ’\mathrm{1}=\mathrm{2}^{\boldsymbol{\mathrm{x}}} \\ $$$$\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{x}} \\ $$

Question Number 171064    Answers: 2   Comments: 0

When A^(βˆ’1) = [(3,1),(8,4) ] find the A=? ,∣A^(βˆ’1) βˆ£βˆ™A=?

$${When}\:\:{A}^{βˆ’\mathrm{1}} =\begin{bmatrix}{\mathrm{3}}&{\mathrm{1}}\\{\mathrm{8}}&{\mathrm{4}}\end{bmatrix} \\ $$$${find}\:{the}\:\:{A}=?\:,\mid{A}^{βˆ’\mathrm{1}} \mid\centerdot{A}=? \\ $$

Question Number 171046    Answers: 2   Comments: 0

Question Number 171044    Answers: 1   Comments: 3

Is the Light a matter?

$${Is}\:{the}\:{Light}\:{a}\:{matter}? \\ $$

Question Number 171043    Answers: 1   Comments: 0

A∈R A=(((√(xβˆ’2))+x+3)/( (√(4βˆ’2x))+xβˆ’1)) faind A=?

$${A}\in{R} \\ $$$${A}=\frac{\sqrt{{x}βˆ’\mathrm{2}}+{x}+\mathrm{3}}{\:\sqrt{\mathrm{4}βˆ’\mathrm{2}{x}}+{x}βˆ’\mathrm{1}}\:\:\:\:\:\:\:\:\:\:{faind}\:{A}=? \\ $$

Question Number 171034    Answers: 0   Comments: 2

Question Number 171033    Answers: 2   Comments: 1

lim_(xβ†’0) (1/x) [ ((((1βˆ’(√(1βˆ’x)))/( (√(1+x))βˆ’1)) ))^(1/3) βˆ’1 ]=?

$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{{x}}\:\left[\:\sqrt[{\mathrm{3}}]{\frac{\mathrm{1}βˆ’\sqrt{\mathrm{1}βˆ’{x}}}{\:\sqrt{\mathrm{1}+{x}}βˆ’\mathrm{1}}\:}βˆ’\mathrm{1}\:\right]=? \\ $$

Question Number 171032    Answers: 1   Comments: 0

Find the domain and range of the function, f(x)=((x^2 +2)/(2x+1)) Mastermind

$${Find}\:{the}\:{domain}\:{and}\:{range}\:{of}\:{the} \\ $$$${function},\:{f}\left({x}\right)=\frac{{x}^{\mathrm{2}} +\mathrm{2}}{\mathrm{2}{x}+\mathrm{1}} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171031    Answers: 1   Comments: 0

Question Number 171025    Answers: 2   Comments: 0

Question Number 171023    Answers: 0   Comments: 0

Question Number 171038    Answers: 2   Comments: 0

Question Number 171021    Answers: 0   Comments: 0

Question Number 171039    Answers: 1   Comments: 0

I_n =∫_0 ^1 (1βˆ’u)^n (√(ud(u))) Demonstrate that βˆ€n∈N, I_n β‰₯0

$${I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}βˆ’{u}\right)^{{n}} \sqrt{{ud}\left({u}\right)} \\ $$$${Demonstrate}\:{that}\:\forall{n}\in{N},\:{I}_{{n}} \geq\mathrm{0} \\ $$

Question Number 176906    Answers: 1   Comments: 3

Question Number 171014    Answers: 1   Comments: 0

Question Number 182219    Answers: 1   Comments: 0

Question Number 171012    Answers: 1   Comments: 1

The number of five digits can be made with the digits 1, 2, 3 each of which can be used atmost thrice in a number is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{five}\:\mathrm{digits}\:\mathrm{can}\:\mathrm{be}\:\mathrm{made} \\ $$$$\mathrm{with}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{1},\:\mathrm{2},\:\mathrm{3}\:\mathrm{each}\:\mathrm{of}\:\mathrm{which}\:\mathrm{can} \\ $$$$\mathrm{be}\:\mathrm{used}\:\mathrm{atmost}\:\mathrm{thrice}\:\mathrm{in}\:\mathrm{a}\:\mathrm{number}\:\mathrm{is} \\ $$

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