Question and Answers Forum

All Questions Topic List

AllQuestion and Answers: Page 1709

Question Number 35117 Answers: 1 Comments: 0

∫((2x+3)/(x^4 −3x−2))dx

$$\int\frac{\mathrm{2}{x}+\mathrm{3}}{{x}^{\mathrm{4}} −\mathrm{3}{x}−\mathrm{2}}{dx} \\ $$

Question Number 35124 Answers: 0 Comments: 9

Question Number 35115 Answers: 0 Comments: 2

Question Number 35101 Answers: 2 Comments: 1

Find volume enclosed by (x^2 /a^2 )+(y^2 /b^2 )+(z^2 /c^2 )=1 .

$${Find}\:{volume}\:{enclosed}\:{by} \\ $$$$\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }+\frac{{z}^{\mathrm{2}} }{{c}^{\mathrm{2}} }=\mathrm{1}\:\:. \\ $$

Question Number 35092 Answers: 0 Comments: 0

Question Number 35088 Answers: 0 Comments: 2

a son and father do a work in 24 day . if both work together and father work last 6 day only then they how much do

$$\boldsymbol{{a}}\:\boldsymbol{{son}}\:\boldsymbol{{and}}\:\boldsymbol{{father}}\:\boldsymbol{{do}}\:\boldsymbol{{a}}\:\boldsymbol{{work}}\:\boldsymbol{{in}} \\ $$$$\mathrm{24}\:\boldsymbol{{day}}\:.\:\boldsymbol{{if}}\:\boldsymbol{{both}}\:\boldsymbol{{work}}\:\boldsymbol{{together}} \\ $$$$\boldsymbol{{and}}\:\boldsymbol{{father}}\:\boldsymbol{{work}}\:\boldsymbol{{last}}\:\mathrm{6}\:\boldsymbol{{day}}\:\boldsymbol{{only}} \\ $$$$\boldsymbol{{then}}\:\boldsymbol{{they}}\:\boldsymbol{{how}}\:\boldsymbol{{much}}\:\boldsymbol{{do}} \\ $$

Question Number 35084 Answers: 1 Comments: 1

Question Number 35080 Answers: 2 Comments: 0

If (a/(b+c)) +(b/(c+a)) +(c/(a+b))=1 then prove that (a^2 /(b+c)) +(b^2 /(c+a)) +(c^2 /(a+b))=0

$${If}\:\frac{{a}}{{b}+{c}}\:+\frac{{b}}{{c}+{a}}\:+\frac{{c}}{{a}+{b}}=\mathrm{1}\:{then}\:{prove}\:{that} \\ $$$$\frac{{a}^{\mathrm{2}} }{{b}+{c}}\:+\frac{{b}^{\mathrm{2}} }{{c}+{a}}\:+\frac{{c}^{\mathrm{2}} }{{a}+{b}}=\mathrm{0} \\ $$

Question Number 35072 Answers: 0 Comments: 2

An n-digit decimal number has been conveerted into octal number.Say it has m digits.What are possible minimum and maximum values of m in terms of n?

$$\mathrm{An}\:\mathrm{n}-\mathrm{digit}\:\mathrm{decimal}\:\mathrm{number}\:\mathrm{has}\:\mathrm{been} \\ $$$$\mathrm{conveerted}\:\mathrm{into}\:\mathrm{octal}\:\mathrm{number}.\mathrm{Say}\:\mathrm{it} \\ $$$$\mathrm{has}\:\mathrm{m}\:\mathrm{digits}.\mathrm{What}\:\mathrm{are}\:\mathrm{possible}\:\:\mathrm{minimum}\: \\ $$$$\mathrm{and}\:\mathrm{maximum}\:\mathrm{values}\:\mathrm{of}\:\mathrm{m}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of} \\ $$$$\mathrm{n}? \\ $$

Question Number 35071 Answers: 1 Comments: 0

A 20-digit decimal number has been converted into octal system.Say it has n digits. What can be minimum and maximum possible values of n?

$$\mathrm{A}\:\mathrm{20}-\mathrm{digit}\:\mathrm{decimal}\:\mathrm{number}\:\mathrm{has}\:\mathrm{been} \\ $$$$\mathrm{converted}\:\mathrm{into}\:\mathrm{octal}\:\mathrm{system}.\mathrm{Say}\:\mathrm{it}\:\mathrm{has}\: \\ $$$$\mathrm{n}\:\mathrm{digits}.\:\mathrm{What}\:\mathrm{can}\:\mathrm{be}\:\mathrm{minimum}\:\mathrm{and} \\ $$$$\mathrm{maximum}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\mathrm{n}? \\ $$$$ \\ $$

Question Number 35062 Answers: 0 Comments: 0

calculate A_n = ∫_0 ^∞ (dt/((t^4 +1)^n )) with n integr natural .

$${calculate}\:{A}_{{n}} \:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dt}}{\left({t}^{\mathrm{4}} \:+\mathrm{1}\right)^{{n}} } \\ $$$${with}\:{n}\:{integr}\:{natural}\:. \\ $$

Question Number 35061 Answers: 2 Comments: 1

find ∫_0 ^∞ ((x^2 +3)/((x^4 +1)^2 ))dx

$${find}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\:\frac{{x}^{\mathrm{2}} \:+\mathrm{3}}{\left({x}^{\mathrm{4}} \:+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 35060 Answers: 1 Comments: 1

calculate ∫_0 ^(π/4) sinx ln(cosx)dx

$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{sinx}\:{ln}\left({cosx}\right){dx} \\ $$

Question Number 35059 Answers: 2 Comments: 2

find ∫_0 ^π (dx/(cosx +sinx))

$${find}\:\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\:\:\frac{{dx}}{{cosx}\:+{sinx}} \\ $$

Question Number 35058 Answers: 1 Comments: 1

find ∫_0 ^(π/4) (dt/((1+cos^2 t)^3 ))

$${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\:\frac{{dt}}{\left(\mathrm{1}+{cos}^{\mathrm{2}} {t}\right)^{\mathrm{3}} } \\ $$

Question Number 35057 Answers: 0 Comments: 1

let u_n =((n/(n+1)))^(1/n) −1 find the nature of Σ_(n≥0) u_n

$${let}\:{u}_{{n}} =\left(\frac{{n}}{{n}+\mathrm{1}}\right)^{\frac{\mathrm{1}}{{n}}} \:\:−\mathrm{1} \\ $$$${find}\:{the}\:{nature}\:{of}\:\sum_{{n}\geqslant\mathrm{0}} {u}_{{n}} \\ $$

Question Number 35056 Answers: 0 Comments: 2

let p(x)=(1+jx)^n −(1−jx)^n 1) find the roots of p(x) 2)factorize p(x) inside C[x] j =e^(i((2π)/3)) .

$${let}\:{p}\left({x}\right)=\left(\mathrm{1}+{jx}\right)^{{n}} \:−\left(\mathrm{1}−{jx}\right)^{{n}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){factorize}\:{p}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$${j}\:={e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{3}}} \:. \\ $$

Question Number 35055 Answers: 1 Comments: 2

calculate ∫_(−∞) ^(+∞) (dx/((1+x+x^2 )^3 ))

$${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} } \\ $$

Question Number 35054 Answers: 0 Comments: 1

find ∫_0 ^(π/4) ((xdx)/(2 +cosx))

$${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\:\frac{{xdx}}{\mathrm{2}\:+{cosx}} \\ $$

Question Number 35053 Answers: 0 Comments: 0

let v(x)=ln(1+x+x^2 ) developp f at integr serie.

$${let}\:{v}\left({x}\right)={ln}\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} \right) \\ $$$${developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$

Question Number 35052 Answers: 0 Comments: 1

let f(x) = (x/(x^2 +x−1)) developp f atintegr serie

$${let}\:{f}\left({x}\right)\:=\:\:\frac{{x}}{{x}^{\mathrm{2}} \:+{x}−\mathrm{1}} \\ $$$${developp}\:{f}\:{atintegr}\:{serie} \\ $$

Question Number 35051 Answers: 0 Comments: 1

calculate Σ_(n=0) ^∞ ((n+3)/(2n+1))x^n

$${calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{{n}+\mathrm{3}}{\mathrm{2}{n}+\mathrm{1}}{x}^{{n}} \\ $$$$ \\ $$

Question Number 35050 Answers: 0 Comments: 0

calculate Σ_(n=0) ^∞ (((−1)^n x^(2n+1) )/(4n^2 −1))

$${calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} \:\:{x}^{\mathrm{2}{n}+\mathrm{1}} }{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}} \\ $$

Question Number 35049 Answers: 1 Comments: 1

let A_n = ∫_(1/n) ^n (1+(1/x^2 ))arctanx dx 1) calculate A_n 2) find lim_(n→+∞) A_n

$${let}\:{A}_{{n}} \:=\:\int_{\frac{\mathrm{1}}{{n}}} ^{{n}} \:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){arctanx}\:{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$

Question Number 35048 Answers: 0 Comments: 0

find ∫ (dx/(cos(sinx)))

$${find}\:\int\:\:\:\:\:\frac{{dx}}{{cos}\left({sinx}\right)} \\ $$

Question Number 35046 Answers: 0 Comments: 0

find F(x)= ∫_0 ^π ln( 1+x sin^2 t)dt with ∣x∣<1 2) calculate ∫_0 ^π ln(1+(1/2)sin^2 t)dt

$${find}\:{F}\left({x}\right)=\:\int_{\mathrm{0}} ^{\pi} \:{ln}\left(\:\mathrm{1}+{x}\:{sin}^{\mathrm{2}} {t}\right){dt}\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}{sin}^{\mathrm{2}} {t}\right){dt} \\ $$

Pg 1704 Pg 1705 Pg 1706 Pg 1707 Pg 1708 Pg 1709 Pg 1710 Pg 1711 Pg 1712 Pg 1713

Contact: info@tinkutara.com