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AllQuestion and Answers: Page 1703

Question Number 30423 Answers: 0 Comments: 0

study the convergence of ∫_0 ^∞ ((sint)/t^α )dt . αfrom R.

$${study}\:{the}\:{convergence}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sint}}{{t}^{\alpha} }{dt}\:.\:\alpha{from}\:{R}. \\ $$

Question Number 30422 Answers: 0 Comments: 0

integrate the d.e. y^′ 2ty= sint

$${integrate}\:{the}\:{d}.{e}.\:{y}^{'} \:\mathrm{2}{ty}=\:{sint} \\ $$

Question Number 30421 Answers: 1 Comments: 0

integrate y^′ −2ty +ty^2 =0

$${integrate}\:{y}^{'} −\mathrm{2}{ty}\:+{ty}^{\mathrm{2}} =\mathrm{0} \\ $$

Question Number 30420 Answers: 1 Comments: 0

integrate y^(′′) = (1/2)(√(1+(y^′ )^2 )) .

$${integrate}\:{y}^{''} =\:\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{1}+\left({y}^{'} \right)^{\mathrm{2}} }\:\:\:\:\:. \\ $$

Question Number 30419 Answers: 1 Comments: 0

integrate (1+x^2 )y^′ +xy −2x=0 with cond.y(1)=0

$${integrate}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}^{'} \:+{xy}\:−\mathrm{2}{x}=\mathrm{0}\:{with}\:{cond}.{y}\left(\mathrm{1}\right)=\mathrm{0} \\ $$

Question Number 30418 Answers: 0 Comments: 0

integrate y^′ −2xy = sinx e^x^2 with y(0)=1.

$${integrate}\:{y}^{'} \:−\mathrm{2}{xy}\:=\:{sinx}\:{e}^{{x}^{\mathrm{2}} } \:{with}\:{y}\left(\mathrm{0}\right)=\mathrm{1}. \\ $$

Question Number 30417 Answers: 0 Comments: 0

integrate the d.e. (1+x^2 )y^′ −2x y = e^(−x^2 ) .

$${integrate}\:{the}\:{d}.{e}.\:\:\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}^{'} \:−\mathrm{2}{x}\:{y}\:=\:{e}^{−{x}^{\mathrm{2}} } . \\ $$

Question Number 30416 Answers: 0 Comments: 0

integrate the d.e. y^(′′) −4y =x +e^(2x) .

$${integrate}\:{the}\:{d}.{e}.\:\:\:{y}^{''} \:−\mathrm{4}{y}\:={x}\:+{e}^{\mathrm{2}{x}} . \\ $$

Question Number 30415 Answers: 0 Comments: 0

find the value of Σ_(k=0) ^n (1/(k+1)) C_n ^k .

$${find}\:{the}\:{value}\:{of}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\frac{\mathrm{1}}{{k}+\mathrm{1}}\:{C}_{{n}} ^{{k}} \:\:. \\ $$

Question Number 30414 Answers: 0 Comments: 0

find the value of Σ_(p=0) ^n (−1)^(p ) (C_n ^p /(p+1)) .

$${find}\:\:{the}\:{value}\:{of}\:\:\sum_{{p}=\mathrm{0}} ^{{n}} \:\left(−\mathrm{1}\right)^{{p}\:\:} \:\frac{{C}_{{n}} ^{{p}} }{{p}+\mathrm{1}}\:. \\ $$

Question Number 30413 Answers: 0 Comments: 0

study the convergence of A(α)= ∫_0 ^∞ ((ln(t) arctant)/t^α )dt

$${study}\:{the}\:{convergence}\:{of}\:\:{A}\left(\alpha\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}\left({t}\right)\:{arctant}}{{t}^{\alpha} }{dt} \\ $$

Question Number 30412 Answers: 0 Comments: 0

f is a function increazing(or decreazing)on ]0,1] prove that lim_(n→∞) (1/n)Σ_(q=1) ^n f((q/n))=∫_0 ^1 f(t)dt.

$$\left.{f}\left.\:{is}\:{a}\:{function}\:{increazing}\left({or}\:{decreazing}\right){on}\:\right]\mathrm{0},\mathrm{1}\right] \\ $$$${prove}\:{that}\:{lim}_{{n}\rightarrow\infty} \:\frac{\mathrm{1}}{{n}}\sum_{{q}=\mathrm{1}} ^{{n}} {f}\left(\frac{{q}}{{n}}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({t}\right){dt}. \\ $$$$ \\ $$

Question Number 30411 Answers: 0 Comments: 0

solve the d.e. y+x (y^′ )^3 =0

$${solve}\:{the}\:{d}.{e}.\:{y}+{x}\:\left({y}^{'} \right)^{\mathrm{3}} =\mathrm{0} \\ $$

Question Number 30409 Answers: 0 Comments: 0

find lim_(n→∞) Σ_(1≤i<j≤n) x^(i+j) .with ∣x∣<1 .

$${find}\:{lim}_{{n}\rightarrow\infty} \:\:\sum_{\mathrm{1}\leqslant{i}<{j}\leqslant{n}} \:\:{x}^{{i}+{j}} \:\:.{with}\:\mid{x}\mid<\mathrm{1}\:\:. \\ $$

Question Number 30408 Answers: 0 Comments: 0

integrate the d.e. y^′ sinx −2y cosx=e^(−x) .

$${integrate}\:{the}\:{d}.{e}.\:{y}^{'} {sinx}\:−\mathrm{2}{y}\:{cosx}={e}^{−{x}} . \\ $$

Question Number 30407 Answers: 0 Comments: 0

let give s(x)= Σ_(n=1) ^∞ nx^n and w(x)=Σ_(n=1) ^∞ (1/n)x^(n−1) for∣x∣<1 find s(x).w(x) at form of series 2) find s(x).w(x) at form of function.

$${let}\:{give}\:{s}\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\infty} {nx}^{{n}} \:\:{and}\:{w}\left({x}\right)=\sum_{{n}=\mathrm{1}} ^{\infty} \frac{\mathrm{1}}{{n}}{x}^{{n}−\mathrm{1}} \:\:{for}\mid{x}\mid<\mathrm{1} \\ $$$${find}\:{s}\left({x}\right).{w}\left({x}\right)\:{at}\:{form}\:{of}\:{series} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{s}\left({x}\right).{w}\left({x}\right)\:{at}\:{form}\:{of}\:{function}. \\ $$

Question Number 30425 Answers: 1 Comments: 0

decompose inside R[x] F(x)= (x^(2n) /((x^2 +1)^n )) with n from N and n>0.

$${decompose}\:{inside}\:{R}\left[{x}\right]\: \\ $$$${F}\left({x}\right)=\:\:\:\frac{{x}^{\mathrm{2}{n}} }{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{{n}} }\:\:\:{with}\:{n}\:{from}\:{N}\:{and}\:{n}>\mathrm{0}. \\ $$

Question Number 30405 Answers: 1 Comments: 0

x^2 +y^2 =13 x^2 −3xy+y^2 =35 find the value of x and y

$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{13} \\ $$$${x}^{\mathrm{2}} −\mathrm{3}{xy}+{y}^{\mathrm{2}} =\mathrm{35} \\ $$$${find}\:{the}\:{value}\:{of}\:{x}\:{and}\:{y} \\ $$

Question Number 30401 Answers: 0 Comments: 0

is there exists a onto group homo from D4 to Z4?

$${is}\:{there}\:{exists}\:{a}\:{onto}\:{group}\:{homo}\:{from}\:{D}\mathrm{4}\:{to}\:{Z}\mathrm{4}? \\ $$

Question Number 30390 Answers: 0 Comments: 5

Question Number 30377 Answers: 1 Comments: 1

Question Number 30373 Answers: 0 Comments: 4

Question Number 30436 Answers: 1 Comments: 1

let ϕ(x)=1−2^(1−x) prove that ϕ(x)=(x−1)ln2 −(((ln2)^2 )/2)(x−1)^2 +o((x−1)^2 ).

$${let}\:\varphi\left({x}\right)=\mathrm{1}−\mathrm{2}^{\mathrm{1}−{x}} \:\:{prove}\:{that} \\ $$$$\varphi\left({x}\right)=\left({x}−\mathrm{1}\right){ln}\mathrm{2}\:−\frac{\left({ln}\mathrm{2}\right)^{\mathrm{2}} }{\mathrm{2}}\left({x}−\mathrm{1}\right)^{\mathrm{2}} \:+{o}\left(\left({x}−\mathrm{1}\right)^{\mathrm{2}} \right). \\ $$

Question Number 30367 Answers: 0 Comments: 7

Question Number 30366 Answers: 0 Comments: 1

Question Number 30364 Answers: 1 Comments: 2

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