Question and Answers Forum

AllQuestion and Answers: Page 66

Question Number 216411 Answers: 1 Comments: 0

(dx/dx)

Question Number 216408 Answers: 0 Comments: 1

∫_(−1) ^1 (1/x)(√((1+x)/(1−x)))ln(((2x^2 +2x+1)/(2x^2 −2x+1)))dx

$$\int_{−\mathrm{1}} ^{\mathrm{1}} \frac{\mathrm{1}}{{x}}\sqrt{\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}}\mathrm{ln}\left(\frac{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}}\right){dx} \\ $$

Question Number 216390 Answers: 0 Comments: 3

f(x)=ax

$${f}\left({x}\right)={ax}\: \\ $$

Question Number 216381 Answers: 1 Comments: 0

∫(lnx)^2 dx

$$\int\left({lnx}\right)^{\mathrm{2}} {dx} \\ $$

Question Number 216388 Answers: 1 Comments: 1

Question Number 216387 Answers: 1 Comments: 0

Question Number 216372 Answers: 2 Comments: 0

∫((xe^x )/((x+1)^2 ))dx

$$\int\frac{{xe}^{{x}} }{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 216369 Answers: 2 Comments: 0

Question Number 216355 Answers: 1 Comments: 1

given that ϕ,β are the roots of the equation 3x2−x−5=0 from the equation whose roots are 2ϕ−1/β,2β−1/ϕ

$${given}\:{that}\:\varphi,\beta\:{are}\:{the}\:{roots}\:{of}\:{the}\:{equation}\:\mathrm{3}{x}\mathrm{2}−{x}−\mathrm{5}=\mathrm{0}\:{from}\:{the}\:{equation}\:{whose}\:{roots}\:{are}\:\mathrm{2}\varphi−\mathrm{1}/\beta,\mathrm{2}\beta−\mathrm{1}/\varphi \\ $$

Question Number 216352 Answers: 1 Comments: 1

Question Number 216351 Answers: 1 Comments: 0

Vector field F^→ ;R^3 →R^3 F^→ (x,y,z)=xye_1 ^→ −5ye_2 ^→ −3yze_3 ^→ ∫∫_(S;x^2 +y^2 +z^2 =r^2 ) F^→ ∙dS^→ = ?

$$\mathrm{Vector}\:\mathrm{field}\:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}};\mathbb{R}^{\mathrm{3}} \rightarrow\mathbb{R}^{\mathrm{3}} \\ $$$$\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\left({x},{y},{z}\right)={xy}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} −\mathrm{5}{y}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{2}} −\mathrm{3}{yz}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{3}} \\ $$$$\underset{\mathcal{S};{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} ={r}^{\mathrm{2}} } {\int\int}\:\:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\centerdot\mathrm{d}\overset{\rightarrow} {\boldsymbol{\mathrm{S}}}=\:? \\ $$

Question Number 216350 Answers: 1 Comments: 0

S is the boundary surface of the surrounded by the cylinder x^2 +y^2 =9 and plane z=0 , z=2 and and vector Field F^→ ;R^3 →R^3 F^→ (x,y,z)=3ye_1 ^→ +yze_2 ^→ −xyz^5 e_3 ^→ ∫∫_(S) F^→ ∙dS^→ =?

$$\mathcal{S}\:\mathrm{is}\:\mathrm{the}\:\mathrm{boundary}\:\mathrm{surface}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{surrounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{cylinder}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{9} \\ $$$$\mathrm{and}\:\mathrm{plane}\:{z}=\mathrm{0}\:,\:{z}=\mathrm{2}\:\mathrm{and} \\ $$$$\mathrm{and}\:\mathrm{vector}\:\mathrm{Field}\:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}};\mathbb{R}^{\mathrm{3}} \rightarrow\mathbb{R}^{\mathrm{3}} \\ $$$$\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\left({x},{y},{z}\right)=\mathrm{3}{y}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} +{yz}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{2}} −{xyz}^{\mathrm{5}} \overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{3}} \\ $$$$\underset{\mathcal{S}} {\int\int}\:\:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\centerdot\mathrm{d}\overset{\rightarrow} {\boldsymbol{\mathrm{S}}}=? \\ $$

Question Number 216332 Answers: 4 Comments: 0

Question Number 216324 Answers: 1 Comments: 1

Question Number 216323 Answers: 1 Comments: 2

Let 10≥x,y≥0 and x,y∈R Find a)P(x−2>y) b)P(x+2<y)

$$\mathrm{Let}\:\mathrm{10}\geqslant{x},{y}\geqslant\mathrm{0}\:\mathrm{and}\:{x},{y}\in\mathbb{R} \\ $$$$\mathrm{Find} \\ $$$$\left.{a}\right){P}\left({x}−\mathrm{2}>{y}\right) \\ $$$$\left.{b}\right){P}\left({x}+\mathrm{2}<{y}\right) \\ $$

Question Number 216316 Answers: 2 Comments: 0

Calculer lim_(x→−2) ((x^2 +x−2)/( (√(6+x)) −2))

$$\mathrm{Calculer} \\ $$$$\mathrm{lim}_{\boldsymbol{\mathrm{x}}\rightarrow−\mathrm{2}} \frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}−\mathrm{2}}{\:\sqrt{\mathrm{6}+\boldsymbol{\mathrm{x}}}\:−\mathrm{2}} \\ $$

Question Number 216312 Answers: 2 Comments: 0

If ab^2 + bc^2 + ca^2 = 0 then find ((a/b) + (b/c)) + ((b/c) + (c/a)) + ((c/a) + (a/b)) + 2.

$$\mathrm{If}\:{ab}^{\mathrm{2}} \:+\:{bc}^{\mathrm{2}} \:+\:{ca}^{\mathrm{2}} \:=\:\mathrm{0}\:\mathrm{then}\:\mathrm{find}\: \\ $$$$\left(\frac{{a}}{{b}}\:+\:\frac{{b}}{{c}}\right)\:+\:\left(\frac{{b}}{{c}}\:+\:\frac{{c}}{{a}}\right)\:+\:\left(\frac{{c}}{{a}}\:+\:\frac{{a}}{{b}}\right)\:+\:\mathrm{2}. \\ $$

Question Number 216296 Answers: 0 Comments: 0

Question Number 216284 Answers: 1 Comments: 1

if i have 7200 coin and Each A,B,C are 500 coin at this time how many Should i buy each so that i can buy as many possible???

$$\mathrm{if}\:\mathrm{i}\:\mathrm{have}\:\mathrm{7200}\:\mathrm{coin} \\ $$$$\mathrm{and}\:\mathrm{Each}\:\boldsymbol{\mathrm{A}},\boldsymbol{\mathrm{B}},\boldsymbol{\mathrm{C}}\:\mathrm{are}\:\mathrm{500}\:\mathrm{coin} \\ $$$$\mathrm{at}\:\mathrm{this}\:\mathrm{time}\:\mathrm{how}\:\mathrm{many}\:\mathrm{Should} \\ $$$$\mathrm{i}\:\mathrm{buy}\:\mathrm{each}\:\mathrm{so}\:\mathrm{that}\:\mathrm{i}\:\mathrm{can}\:\mathrm{buy}\:\mathrm{as}\:\mathrm{many} \\ $$$$\mathrm{possible}??? \\ $$

Question Number 216281 Answers: 0 Comments: 4

Prove:∫_0 ^(π/2) dφ∫_0 ^(π/2) f(sinθ cos θ)sinθ dθ=(π/2)∫_0 ^1 f(x)dx

$$\mathrm{Prove}:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {d}\phi\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {f}\left(\mathrm{sin}\theta\:\mathrm{cos}\:\theta\right)\mathrm{sin}\theta\:{d}\theta=\frac{\pi}{\mathrm{2}}\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx} \\ $$

Question Number 216279 Answers: 1 Comments: 3

Question Number 216274 Answers: 0 Comments: 0

prove that : Σ_(n=1) ^∞ (( cos( n ))/n) ( 1+(1/( (√2))) + (1/( (√3))) + ...+(1/( (√n))) ) is convergent.

$$ \\ $$$$\:\:\:{prove}\:{that}\:: \\ $$$$ \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:{cos}\left(\:{n}\:\right)}{{n}}\:\left(\:\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\:+\:...+\frac{\mathrm{1}}{\:\sqrt{{n}}}\:\right) \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:{is}\:\:\:{convergent}. \\ $$$$ \\ $$

Question Number 216270 Answers: 2 Comments: 0

If (b − c)x + (c − a)y + (a − b)z = 0 then prove that ((b − c)/(y − z)) = ((c − a)/(z − x)) = ((a − b)/(x − y)) .

$$\mathrm{If}\:\left({b}\:−\:{c}\right){x}\:+\:\left({c}\:−\:{a}\right){y}\:+\:\left({a}\:−\:{b}\right){z}\:=\:\mathrm{0}\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\frac{{b}\:−\:{c}}{{y}\:−\:{z}}\:=\:\frac{{c}\:−\:{a}}{{z}\:−\:{x}}\:=\:\frac{{a}\:−\:{b}}{{x}\:−\:{y}}\:. \\ $$

Question Number 216266 Answers: 1 Comments: 0

(√2)^((√2)^((√2)^⋰ ) ) =?

$$\sqrt{\mathrm{2}}\:^{\sqrt{\mathrm{2}}\:^{\sqrt{\mathrm{2}}\:^{\iddots} } } =? \\ $$

Question Number 216265 Answers: 0 Comments: 0

Question Number 216263 Answers: 0 Comments: 1

Pg 61 Pg 62 Pg 63 Pg 64 Pg 65 Pg 66 Pg 67 Pg 68 Pg 69 Pg 70

Contact: info@tinkutara.com