Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1440

Question Number 67795    Answers: 0   Comments: 2

let A_p =∫_0 ^π x^p cos(nx)dx 1) calculate A_0 ,A_1 ,A_2 2)determine a relation of recurrence between A_p

$${let}\:\:{A}_{{p}} =\int_{\mathrm{0}} ^{\pi} \:{x}^{{p}} \:{cos}\left({nx}\right){dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{\mathrm{0}} ,{A}_{\mathrm{1}} ,{A}_{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right){determine}\:{a}\:{relation}\:{of}\:{recurrence}\:{between}\:\:{A}_{{p}} \\ $$

Question Number 67775    Answers: 2   Comments: 0

Question Number 67774    Answers: 1   Comments: 0

Question Number 67772    Answers: 2   Comments: 3

Question Number 67770    Answers: 1   Comments: 0

Question Number 67813    Answers: 1   Comments: 8

Question Number 67760    Answers: 0   Comments: 0

y′=y^2 +2 ; y(0)=2 solve by picards iteration method

$${y}'={y}^{\mathrm{2}} +\mathrm{2}\:;\:{y}\left(\mathrm{0}\right)=\mathrm{2} \\ $$$$ \\ $$$${solve}\:{by}\:{picards}\:{iteration}\:{method} \\ $$$$ \\ $$

Question Number 67759    Answers: 0   Comments: 1

using variation of parameters method (x+2)^2 y′′−(x+2)y′=2x+4 x^2 y′′+2xy′−2y=x^2 lnx+3x

$${using}\:{variation}\:{of}\:{parameters}\:{method} \\ $$$$ \\ $$$$\left({x}+\mathrm{2}\right)^{\mathrm{2}} {y}''−\left({x}+\mathrm{2}\right){y}'=\mathrm{2}{x}+\mathrm{4} \\ $$$$ \\ $$$$ \\ $$$${x}^{\mathrm{2}} {y}''+\mathrm{2}{xy}'−\mathrm{2}{y}={x}^{\mathrm{2}} {lnx}+\mathrm{3}{x} \\ $$

Question Number 67761    Answers: 0   Comments: 0

solve by laplace transform method x^(•• ) +w_0 ^2 x=coswt x(0)=x_0 x^• (0)=v_0 w^2 ≠ w_0 ^2

$${solve}\:{by}\:{laplace}\:{transform}\:{method} \\ $$$$ \\ $$$$\overset{\bullet\bullet\:} {{x}}\:+{w}_{\mathrm{0}} ^{\mathrm{2}} {x}={coswt}\:\:\:{x}\left(\mathrm{0}\right)={x}_{\mathrm{0}} \:\overset{\bullet} {{x}}\left(\mathrm{0}\right)={v}_{\mathrm{0}} \:\:\:\:\:{w}^{\mathrm{2}} \neq\:{w}_{\mathrm{0}} ^{\mathrm{2}} \\ $$

Question Number 67762    Answers: 0   Comments: 0

solve by the complex method y^(iv) +3y^3 +2y^2 =−3sin2x y^2 +a^2 y=e^x cosecx

$${solve}\:{by}\:{the}\:{complex}\:{method} \\ $$$$ \\ $$$$ \\ $$$${y}^{{iv}} +\mathrm{3}{y}^{\mathrm{3}} +\mathrm{2}{y}^{\mathrm{2}} =−\mathrm{3}{sin}\mathrm{2}{x} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$${y}^{\mathrm{2}} +{a}^{\mathrm{2}} {y}={e}^{{x}} {cosecx} \\ $$

Question Number 67749    Answers: 1   Comments: 0

Question Number 67745    Answers: 3   Comments: 0

solve the system of equations { ((3∣x−5∣+4=y)),((∣y−3∣=4x−12)) :}

$${solve}\:{the}\:{system}\:{of}\:{equations\begin{cases}{\mathrm{3}\mid{x}−\mathrm{5}\mid+\mathrm{4}={y}}\\{\mid{y}−\mathrm{3}\mid=\mathrm{4}{x}−\mathrm{12}}\end{cases}} \\ $$

Question Number 67744    Answers: 0   Comments: 4

let f(x) =∫_0 ^∞ ((sin(t^2 ))/((x^2 +t^2 )^2 ))dt with x>0 1)determine a explicit form for f(x) 2) find also g(x) =∫_0 ^∞ ((sin(t^2 ))/((x^2 +t^2 )^3 ))dt 3) give f^((n)) (x) at form of integral and calculate f^((n)) (1). 4) find the valueof ∫_0 ^∞ ((sin(t^2 ))/((1+t^2 )^2 )) dt and ∫_0 ^∞ ((sin(t^2 ))/((1+t^2 )^3 ))dt

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left({t}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} \right)^{\mathrm{2}} }{dt}\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right){determine}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left({t}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} \right)^{\mathrm{3}} }{dt} \\ $$$$\left.\mathrm{3}\right)\:{give}\:{f}^{\left({n}\right)} \left({x}\right)\:{at}\:{form}\:{of}\:{integral}\:{and}\:{calculate}\:{f}^{\left({n}\right)} \left(\mathrm{1}\right). \\ $$$$\left.\mathrm{4}\right)\:{find}\:{the}\:{valueof}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left({t}^{\mathrm{2}} \right)}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dt}\:{and}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left({t}^{\mathrm{2}} \right)}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{\mathrm{3}} }{dt} \\ $$

Question Number 67743    Answers: 0   Comments: 0

^

$$\:^{} \\ $$

Question Number 67728    Answers: 1   Comments: 5

Question Number 67719    Answers: 1   Comments: 0

Question Number 67716    Answers: 2   Comments: 0

Question Number 67711    Answers: 0   Comments: 0

Find the value of (1/(cos^2 (10°))) + (1/(sin^2 (20°))) + (1/(sin^2 (40°)))

$${Find}\:\:{the}\:\:{value}\:\:{of} \\ $$$$\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{cos}^{\mathrm{2}} \left(\mathrm{10}°\right)}\:+\:\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{20}°\right)}\:+\:\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{40}°\right)}\: \\ $$

Question Number 67708    Answers: 1   Comments: 0

Question Number 67698    Answers: 0   Comments: 0

Question Number 67697    Answers: 1   Comments: 0

⋓si⋒g ChineseRemainderTheorm ∂etermine polynomial p(x) such that p(x)≡8(mod x+1) p(x)≡−24(mod x+3) p(x)≡6(mod x) p(x)≡0(mod x+2)

$$\Cup\mathrm{si}\Cap\mathrm{g}\:\mathrm{ChineseRemainderTheorm} \\ $$$$\partial\mathrm{etermine}\:\mathrm{polynomial}\:\mathrm{p}\left(\mathrm{x}\right)\:\mathrm{such}\:\mathrm{that} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{p}\left(\mathrm{x}\right)\equiv\mathrm{8}\left(\mathrm{mod}\:\mathrm{x}+\mathrm{1}\right) \\ $$$$\:\:\:\:\:\:\:\:\mathrm{p}\left(\mathrm{x}\right)\equiv−\mathrm{24}\left(\mathrm{mod}\:\mathrm{x}+\mathrm{3}\right) \\ $$$$\:\:\:\:\:\:\:\:\mathrm{p}\left(\mathrm{x}\right)\equiv\mathrm{6}\left(\mathrm{mod}\:\mathrm{x}\right) \\ $$$$\:\:\:\:\:\:\:\:\mathrm{p}\left(\mathrm{x}\right)\equiv\mathrm{0}\left(\mathrm{mod}\:\mathrm{x}+\mathrm{2}\right) \\ $$$$ \\ $$

Question Number 67696    Answers: 0   Comments: 0

∫_0 ^1 (1−x)/(1+x)lnx dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{x}\right)/\left(\mathrm{1}+{x}\right){lnx}\:{dx} \\ $$

Question Number 67692    Answers: 1   Comments: 0

Question Number 67688    Answers: 0   Comments: 1

A relation R defined by _((x,y)) R_((u,v)) ⇔ v^2 −y^2 = u^2 −x^2 show that R is an equivalent Relation.

$${A}\:{relation}\:\mathbb{R}\:{defined}\:{by}\:\:\:_{\left({x},{y}\right)} {R}_{\left({u},{v}\right)} \:\Leftrightarrow\:\:{v}^{\mathrm{2}} −{y}^{\mathrm{2}} \:=\:{u}^{\mathrm{2}} −{x}^{\mathrm{2}} \\ $$$${show}\:{that}\:{R}\:{is}\:{an}\:{equivalent}\:{Relation}. \\ $$

Question Number 67687    Answers: 0   Comments: 3

find the range of values of ∣((x^2 −9)/3_ )∣= ((9−x^2 )/3)

$${find}\:{the}\:{range}\:{of}\:{values}\:{of}\: \\ $$$$\:\:\mid\frac{{x}^{\mathrm{2}} −\mathrm{9}}{\mathrm{3}_{\:} }\mid=\:\frac{\mathrm{9}−{x}^{\mathrm{2}} }{\mathrm{3}} \\ $$$$ \\ $$

Question Number 67686    Answers: 0   Comments: 2

given that the roots of the equation 4x^2 + 6x + 9 =0 are λ and δ where λ = (1 + α^2 +β^2 ) and δ = α^3 + β^3 find an equation whose roots are (1/(αλ)) and (1/(βδ))

$${given}\:{that}\:{the}\:{roots}\:{of}\:{the}\:{equation}\:\:\mathrm{4}{x}^{\mathrm{2}} \:+\:\mathrm{6}{x}\:+\:\mathrm{9}\:=\mathrm{0}\:{are}\:\:\lambda\:{and}\:\delta\:\:{where}\: \\ $$$$\:\lambda\:=\:\left(\mathrm{1}\:+\:\alpha^{\mathrm{2}} \:+\beta^{\mathrm{2}} \right)\:\:{and}\:\:\delta\:=\:\alpha^{\mathrm{3}} \:+\:\beta^{\mathrm{3}} \\ $$$${find}\:{an}\:{equation}\:{whose}\:{roots}\:{are}\: \\ $$$$\:\:\frac{\mathrm{1}}{\alpha\lambda}\:{and}\:\:\frac{\mathrm{1}}{\beta\delta} \\ $$

  Pg 1435      Pg 1436      Pg 1437      Pg 1438      Pg 1439      Pg 1440      Pg 1441      Pg 1442      Pg 1443      Pg 1444   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com