Question and Answers Forum

AllQuestion and Answers: Page 665

Question Number 151043 Answers: 2 Comments: 0

Solve the system: { ((y = ((2x)/(1−x^2 )))),((z = ((2y)/(1−y^2 )))),((x = ((2z)/(1−z^2 )))) :}

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{system}: \\ $$$$\begin{cases}{\boldsymbol{\mathrm{y}}\:=\:\frac{\mathrm{2x}}{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\\{\boldsymbol{\mathrm{z}}\:=\:\frac{\mathrm{2y}}{\mathrm{1}−\mathrm{y}^{\mathrm{2}} }}\\{\boldsymbol{\mathrm{x}}\:=\:\frac{\mathrm{2z}}{\mathrm{1}−\mathrm{z}^{\mathrm{2}} }}\end{cases} \\ $$

Question Number 151042 Answers: 0 Comments: 1

if (√((9)^(1/3) − 1)) + (√(((16))^(1/3) − (4)^(1/3) )) = (√x) ; x∈Z find x=?

$$\mathrm{if}\:\:\sqrt{\sqrt[{\mathrm{3}}]{\mathrm{9}}\:−\:\mathrm{1}}\:+\:\sqrt{\sqrt[{\mathrm{3}}]{\mathrm{16}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{4}}}\:=\:\sqrt{\boldsymbol{\mathrm{x}}}\:\:;\:\:\boldsymbol{\mathrm{x}}\in\mathbb{Z} \\ $$$$\mathrm{find}\:\:\boldsymbol{\mathrm{x}}=? \\ $$

Question Number 151037 Answers: 1 Comments: 0

Σ_(r=1,r≠s) ^n Σ_(s=1) ^n ((rs)/(n(n−1)))=^? (((n+1)(3n+2))/(12))

$$\underset{\mathrm{r}=\mathrm{1},\mathrm{r}\neq\mathrm{s}} {\overset{\mathrm{n}} {\sum}}\:\:\underset{\mathrm{s}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{rs}}{\mathrm{n}\left(\mathrm{n}−\mathrm{1}\right)}\overset{?} {=}\frac{\left(\mathrm{n}+\mathrm{1}\right)\left(\mathrm{3n}+\mathrm{2}\right)}{\mathrm{12}} \\ $$

Question Number 151036 Answers: 0 Comments: 0

$$ \\ $$

Question Number 151034 Answers: 0 Comments: 0

Question Number 151035 Answers: 0 Comments: 0

determinant ((,),(,))

$$\begin{vmatrix}{}&{}\\{}&{}\end{vmatrix} \\ $$

Question Number 151029 Answers: 0 Comments: 0

Question Number 151028 Answers: 1 Comments: 0

Question Number 151026 Answers: 1 Comments: 0

Σ_(n=0) ^∞ (0^n /(n!))=?

$$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{0}^{\mathrm{n}} }{\mathrm{n}!}=? \\ $$

Question Number 151053 Answers: 1 Comments: 0

Question Number 151017 Answers: 0 Comments: 0

∫_0 ^( ∞) (ln(x^(√x) −1))^(−x) dx = ?

$$\: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\left(\mathrm{ln}\left({x}^{\sqrt{{x}}} −\mathrm{1}\right)\right)^{−{x}} \:{dx}\:=\:? \\ $$$$\: \\ $$$$\: \\ $$

Question Number 151015 Answers: 0 Comments: 1

Question Number 151013 Answers: 1 Comments: 0

If log(logx)^(((3log(logx))/(log(log(logx)))) ) = 27 Find x=?

$$\mathrm{If}\:\:\mathrm{log}\left(\mathrm{log}\boldsymbol{\mathrm{x}}\right)^{\frac{\mathrm{3}\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{logx}}\right)}{\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{logx}}\right)\right)}\:} \:=\:\mathrm{27} \\ $$$$\mathrm{Find}\:\:\boldsymbol{\mathrm{x}}=? \\ $$

Question Number 151010 Answers: 1 Comments: 1

Question Number 151001 Answers: 2 Comments: 0

lim_(x→0) ((((2+sin^2 x))^(1/3) −((1+cos 2x))^(1/3) )/(x tan x)) =?

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{2}+\mathrm{sin}\:^{\mathrm{2}} {x}}−\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{cos}\:\mathrm{2}{x}}}{{x}\:\mathrm{tan}\:{x}}\:=?\: \\ $$$$\:\:\: \\ $$

Question Number 150994 Answers: 0 Comments: 0

show that the improper integral lim_(B→∞) ∫_0 ^( B) sin(x)sin(x^2 )dx converges

$$\: \\ $$$$\:\:\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{improper}\:\mathrm{integral} \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\underset{{B}\rightarrow\infty} {\mathrm{lim}}\:\:\int_{\mathrm{0}} ^{\:{B}} \:\mathrm{sin}\left({x}\right)\mathrm{sin}\left({x}^{\mathrm{2}} \right){dx} \\ $$$$\:\: \\ $$$$\:\:\:\mathrm{converges} \\ $$$$\: \\ $$

Question Number 150993 Answers: 1 Comments: 1

∫_0 ^( 1) ((ln(x+1))/(x^2 +1)) dx = ?

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

Question Number 150992 Answers: 2 Comments: 1

∫_0 ^( ∞) (x/(e^x −1)) dx = ?

$$\: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{{x}}{{e}^{{x}} −\mathrm{1}}\:{dx}\:=\:? \\ $$$$\: \\ $$$$\: \\ $$

Question Number 150990 Answers: 1 Comments: 0

I = ∫_(0 ) ^( ∞) (dx/(1+x^n )) = ?

$$\: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{I}\:=\:\int_{\mathrm{0}\:} ^{\:\infty} \:\frac{{dx}}{\mathrm{1}+{x}^{{n}} }\:=\:? \\ $$$$\: \\ $$$$\: \\ $$

Question Number 150986 Answers: 1 Comments: 0

∫_0 ^( 1) ((ln (x+1))/(x^2 +1)) dx = ?

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

Question Number 150984 Answers: 0 Comments: 0

Question Number 151073 Answers: 2 Comments: 0

the value of (((50)),(0) )^2 + (((50)),(1) )^2 + (((50)),(2) )^2 +...+ (((50)),((49)) )^2 + (((50)),((50)) )^2

$$\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\begin{pmatrix}{\mathrm{50}}\\{\mathrm{0}}\end{pmatrix}^{\mathrm{2}} +\begin{pmatrix}{\mathrm{50}}\\{\mathrm{1}}\end{pmatrix}^{\mathrm{2}} +\begin{pmatrix}{\mathrm{50}}\\{\mathrm{2}}\end{pmatrix}^{\mathrm{2}} +...+\begin{pmatrix}{\mathrm{50}}\\{\mathrm{49}}\end{pmatrix}^{\mathrm{2}} +\begin{pmatrix}{\mathrm{50}}\\{\mathrm{50}}\end{pmatrix}^{\mathrm{2}} \\ $$

Question Number 151145 Answers: 1 Comments: 0

Question Number 151144 Answers: 1 Comments: 0

Question Number 150979 Answers: 1 Comments: 0

if x=(4)^(1/3) +(2)^(1/3) +1 find (3/x)+(3/x^2 )+(1/x^3 )=?

$$\mathrm{if}\:\:\mathrm{x}=\sqrt[{\mathrm{3}}]{\mathrm{4}}+\sqrt[{\mathrm{3}}]{\mathrm{2}}+\mathrm{1}\:\:\mathrm{find}\:\:\frac{\mathrm{3}}{\mathrm{x}}+\frac{\mathrm{3}}{\mathrm{x}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }=? \\ $$$$ \\ $$

Question Number 150977 Answers: 1 Comments: 0

Pg 660 Pg 661 Pg 662 Pg 663 Pg 664 Pg 665 Pg 666 Pg 667 Pg 668 Pg 669

Contact: info@tinkutara.com