Question and Answers Forum

All Questions Topic List

AllQuestion and Answers: Page 534

Question Number 166134 Answers: 1 Comments: 0

Question Number 166127 Answers: 0 Comments: 0

Question Number 166125 Answers: 0 Comments: 0

Question Number 166120 Answers: 1 Comments: 2

Question Number 166113 Answers: 2 Comments: 2

prove that 1!=1

$${prove}\:{that}\:\mathrm{1}!=\mathrm{1} \\ $$

Question Number 166112 Answers: 1 Comments: 1

prove that 0!=1

$${prove}\:{that}\:\mathrm{0}!=\mathrm{1} \\ $$

Question Number 166111 Answers: 1 Comments: 0

Question Number 166110 Answers: 1 Comments: 0

Prove that ((( n)),(( 0)) )^2 + ((( n)),(( 1)) )^2 + ((( n)),(( 2)) )^2 + …+ ((( n)),(( n)) )^2 = ((( 2n)),(( n)) )

$$\mathrm{Prove}\:\:\mathrm{that} \\ $$$$\:\begin{pmatrix}{\:{n}}\\{\:\mathrm{0}}\end{pmatrix}^{\mathrm{2}} \:+\:\begin{pmatrix}{\:{n}}\\{\:\mathrm{1}}\end{pmatrix}^{\mathrm{2}} \:+\:\begin{pmatrix}{\:{n}}\\{\:\mathrm{2}}\end{pmatrix}^{\mathrm{2}} \:+\:\ldots+\:\begin{pmatrix}{\:{n}}\\{\:{n}}\end{pmatrix}^{\mathrm{2}} \:\:=\:\:\begin{pmatrix}{\:\mathrm{2}{n}}\\{\:\:{n}}\end{pmatrix} \\ $$

Question Number 166104 Answers: 1 Comments: 0

Question Number 166102 Answers: 1 Comments: 0

Question Number 166241 Answers: 2 Comments: 0

x^5 −1=0 please how do i find for all the values of x?

$$\:\boldsymbol{{x}}^{\mathrm{5}} −\mathrm{1}=\mathrm{0} \\ $$$$\:\boldsymbol{{please}}\:\boldsymbol{{how}}\:\boldsymbol{{do}}\:\boldsymbol{{i}}\:\boldsymbol{{find}}\:\boldsymbol{{for}}\:\boldsymbol{{all}}\:\boldsymbol{{the}} \\ $$$$\:\boldsymbol{{values}}\:\boldsymbol{{of}}\:\boldsymbol{{x}}? \\ $$

Question Number 166093 Answers: 2 Comments: 3

Question Number 166089 Answers: 0 Comments: 3

Question Number 166088 Answers: 0 Comments: 0

Question Number 166087 Answers: 1 Comments: 1

Question Number 166084 Answers: 0 Comments: 0

Question Number 166077 Answers: 0 Comments: 0

find ∫ ((cosx)/(1+cos(x)^(tanx) ))

$${find}\:\int\:\frac{{cosx}}{\mathrm{1}+{cos}\left({x}\right)^{{tanx}} } \\ $$

Question Number 166082 Answers: 1 Comments: 0

prove Ω = ∫_0 ^( 1) (( (1−x )^( 2) .ln^( 3) (1−x ))/x) dx = ((51)/8) −(π^( 4) /(15)) ■ m.n

$$ \\ $$$$\:\:\:\:\:\:\:{prove} \\ $$$$\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\left(\mathrm{1}−{x}\:\right)^{\:\mathrm{2}} .{ln}^{\:\mathrm{3}} \left(\mathrm{1}−{x}\:\right)}{{x}}\:{dx}\:=\:\frac{\mathrm{51}}{\mathrm{8}}\:−\frac{\pi^{\:\mathrm{4}} }{\mathrm{15}}\:\:\:\:\:\:\:\:\:\:\:\:\:\blacksquare\:{m}.{n} \\ $$$$\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 166075 Answers: 0 Comments: 1

find the domain and range of the relation {(x,y):∣x∣+y≥2} by draw its graph

$$\mathrm{find}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{and}\:\mathrm{range}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{relation}\:\left\{\left(\mathrm{x},\mathrm{y}\right):\mid\mathrm{x}\mid+\mathrm{y}\geq\mathrm{2}\right\}\:\mathrm{by}\:\mathrm{draw}\:\mathrm{its}\:\mathrm{graph} \\ $$

Question Number 166070 Answers: 0 Comments: 1

Question Number 166067 Answers: 0 Comments: 2

Question Number 166180 Answers: 0 Comments: 0

prove that 𝛗=∫_0 ^( 1) (( ln^( 2) (1−x ))/x^( 2) ) dx = 2 ζ (2) −−−proof−−− 𝛗= [((−1)/x) ln^( 2) (1−x) ]_0 ^1 −∫_0 ^( 1) ((2ln(1−x))/(x(1−x)))dx =−lim_( ξ→1^− ) (1/ξ)ln^( 2) (1−ξ)−2{ ∫_0 ^( 1) ((ln(1−x))/(1−x))dx+∫_0 ^( 1) ((ln(1−x))/x)dx} = −lim_( ξ→1^− ) {(1/ξ)ln^( 2) (1−ξ)+ln^( 2) (1 −ξ)}+2 ζ(2) =lim_(ξ→1^− ) (((ξ−1)/ξ))ln^( 2) (1−ξ) +2ζ(2) =_(ξ→1^− , δ→0^( +) ) ^(1−ξ= δ) [lim_( δ→0^( +) ) (((−δ)/(1−δ)))ln^2 (δ)=0] +2ζ(2) ■ m.n ∴ 𝛗 = 2 ζ(2)

$$ \\ $$$$\:\:\:\:\:\:{prove}\:\:{that} \\ $$$$\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{ln}^{\:\mathrm{2}} \left(\mathrm{1}−{x}\:\right)}{{x}^{\:\mathrm{2}} }\:{dx}\:=\:\mathrm{2}\:\zeta\:\left(\mathrm{2}\right) \\ $$$$\:\:\:\:\:\:−−−{proof}−−− \\ $$$$\:\:\:\:\boldsymbol{\phi}=\:\left[\frac{−\mathrm{1}}{{x}}\:{ln}^{\:\mathrm{2}} \left(\mathrm{1}−{x}\right)\:\right]_{\mathrm{0}} ^{\mathrm{1}} −\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{2}{ln}\left(\mathrm{1}−{x}\right)}{{x}\left(\mathrm{1}−{x}\right)}{dx} \\ $$$$\:\:\:\:\:\:\:\:=−{lim}_{\:\xi\rightarrow\mathrm{1}^{−} } \frac{\mathrm{1}}{\xi}{ln}^{\:\mathrm{2}} \left(\mathrm{1}−\xi\right)−\mathrm{2}\left\{\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}−{x}\right)}{\mathrm{1}−{x}}{dx}+\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}−{x}\right)}{{x}}{dx}\right\} \\ $$$$\:\:\:\:\:\:\:=\:−{lim}_{\:\xi\rightarrow\mathrm{1}^{−} } \left\{\frac{\mathrm{1}}{\xi}{ln}^{\:\mathrm{2}} \left(\mathrm{1}−\xi\right)+{ln}^{\:\mathrm{2}} \left(\mathrm{1}\:−\xi\right)\right\}+\mathrm{2}\:\zeta\left(\mathrm{2}\right) \\ $$$$\:\:\:\:\:\:\:\:={lim}_{\xi\rightarrow\mathrm{1}^{−} } \left(\frac{\xi−\mathrm{1}}{\xi}\right){ln}^{\:\mathrm{2}} \left(\mathrm{1}−\xi\right)\:+\mathrm{2}\zeta\left(\mathrm{2}\right) \\ $$$$\:\:\underset{\xi\rightarrow\mathrm{1}^{−} \:,\:\delta\rightarrow\mathrm{0}^{\:+} } {\overset{\mathrm{1}−\xi=\:\delta} {=}}\left[{lim}_{\:\delta\rightarrow\mathrm{0}^{\:+} } \left(\frac{−\delta}{\mathrm{1}−\delta}\right){ln}^{\mathrm{2}} \left(\delta\right)=\mathrm{0}\right]\:+\mathrm{2}\zeta\left(\mathrm{2}\right)\:\:\:\:\blacksquare\:{m}.{n} \\ $$$$\:\:\:\:\:\:\:\therefore\:\:\:\boldsymbol{\phi}\:=\:\mathrm{2}\:\zeta\left(\mathrm{2}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 166063 Answers: 0 Comments: 2

Question Number 166058 Answers: 1 Comments: 0

Question Number 166053 Answers: 1 Comments: 1

Find x in R:^ x^(√2) + x = 6 (How to solve?)

$$\:\boldsymbol{\mathrm{Find}}\:\:\boldsymbol{\mathrm{x}}\:\:\boldsymbol{\mathrm{in}}\:\:\mathbb{R}\overset{\:} {:} \\ $$$$\: \\ $$$$\:\boldsymbol{\mathrm{x}}^{\sqrt{\mathrm{2}}} \:\:+\:\:\boldsymbol{\mathrm{x}}\:\:=\:\:\mathrm{6}\:\:\:\:\:\left(\boldsymbol{\mathrm{How}}\:\:\boldsymbol{\mathrm{to}}\:\:\boldsymbol{\mathrm{solve}}?\right) \\ $$

Question Number 166049 Answers: 0 Comments: 0

nε R/{0,1} montrer que Σ_(k=n) ^(2n) (x^k /(nx+ln(k)))>=(1/4)

$${n}\epsilon\:{R}/\left\{\mathrm{0},\mathrm{1}\right\}\:{montrer}\:{que} \\ $$$$\underset{{k}={n}} {\overset{\mathrm{2}{n}} {\sum}}\:\frac{{x}^{{k}} }{{nx}+{ln}\left({k}\right)}>=\frac{\mathrm{1}}{\mathrm{4}} \\ $$

Pg 529 Pg 530 Pg 531 Pg 532 Pg 533 Pg 534 Pg 535 Pg 536 Pg 537 Pg 538

Contact: info@tinkutara.com