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Question Number 166160 Answers: 3 Comments: 0

Σ_(n=1) ^∞ Σ_(m=1) ^∞ (1/(m^2 n+mn^2 +2mn))=?

$$\:\:\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\underset{\mathrm{m}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{m}^{\mathrm{2}} \mathrm{n}+\mathrm{mn}^{\mathrm{2}} +\mathrm{2mn}}=? \\ $$

Question Number 166143 Answers: 1 Comments: 0

Question Number 166141 Answers: 2 Comments: 0

∫_0 ^x (t^2 /( (√(a+2t^2 ))))dt

$$\int_{\mathrm{0}} ^{\boldsymbol{\mathrm{x}}} \frac{\boldsymbol{\mathrm{t}}^{\mathrm{2}} }{\:\sqrt{\boldsymbol{\mathrm{a}}+\mathrm{2}\boldsymbol{\mathrm{t}}^{\mathrm{2}} }}\boldsymbol{\mathrm{dt}}\: \\ $$

Question Number 166137 Answers: 2 Comments: 0

Question Number 166135 Answers: 1 Comments: 1

find the domain of f(x) = (1/([x]−1))

$${find}\:{the}\:{domain}\:{of}\:{f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\left[{x}\right]−\mathrm{1}} \\ $$

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

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