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Question Number 73518 Answers: 1 Comments: 1

Question Number 73503 Answers: 1 Comments: 2

Question Number 73619 Answers: 0 Comments: 16

Question Number 73499 Answers: 0 Comments: 2

Question Number 73495 Answers: 1 Comments: 0

(d^2 y/dx^2 )=c^2 x^2 y (y=a , x=0 )

$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }={c}^{\mathrm{2}} {x}^{\mathrm{2}} {y}\:\:\:\:\:\left({y}={a}\:,\:{x}=\mathrm{0}\:\right) \\ $$

Question Number 73491 Answers: 0 Comments: 1

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

$${calculate}\:\int_{−\infty} ^{+\infty} \:\:{e}^{−\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}{x}} \:{dx} \\ $$

Question Number 73490 Answers: 0 Comments: 0

calculate f(a) =∫_0 ^∞ e^(−(x^2 +(a/x^2 ))) dx with a>0

$${calculate}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\left({x}^{\mathrm{2}} \:+\frac{{a}}{{x}^{\mathrm{2}} }\right)} {dx}\:\:{with}\:{a}>\mathrm{0} \\ $$

Question Number 73489 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((arctan(3+x^2 ))/((2 x^2 +9)^2 ))dx

$${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{arctan}\left(\mathrm{3}+{x}^{\mathrm{2}} \right)}{\left(\mathrm{2}\:{x}^{\mathrm{2}} +\mathrm{9}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 73488 Answers: 2 Comments: 1

solve xy^(′′) +(x^2 −1)y^′ =x e^(−x^2 )

$${solve}\:\:\:{xy}^{''} \:\:+\left({x}^{\mathrm{2}} −\mathrm{1}\right){y}^{'} \:\:={x}\:{e}^{−{x}^{\mathrm{2}} } \\ $$

Question Number 73487 Answers: 0 Comments: 1

let α and β roots of the equation x^2 −x+2=0 simplify A_p = α^p +β^p and calculate Σ_(p=0) ^(n−1) A_p and Σ_(p=0) ^(n−1) A_p ^2

$${let}\:\:\:\:\alpha\:{and}\:\beta\:{roots}\:{of}\:\:{the}\:{equation}\:\:{x}^{\mathrm{2}} −{x}+\mathrm{2}=\mathrm{0} \\ $$$${simplify}\:\:\:{A}_{{p}} =\:\alpha^{{p}} \:+\beta^{{p}} \:{and}\:{calculate} \\ $$$$\sum_{{p}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{A}_{{p}} \:\:{and}\:\sum_{{p}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:{A}_{{p}} ^{\mathrm{2}} \\ $$

Question Number 73486 Answers: 0 Comments: 2

let P(x)=(1+ix)^n −(1−ix)^n with n integr decompose the Fraction F (x)=(1/(P(x)))

$${let}\:{P}\left({x}\right)=\left(\mathrm{1}+{ix}\right)^{{n}} −\left(\mathrm{1}−{ix}\right)^{{n}} \:{with}\:{n}\:{integr} \\ $$$${decompose}\:{the}\:{Fraction}\:{F}\:\left({x}\right)=\frac{\mathrm{1}}{{P}\left({x}\right)} \\ $$

Question Number 73485 Answers: 0 Comments: 0

find the roots of P(x)=(1+ix +jx^2 )^n −1 with j =e^(i((2π)/3)) then factorize P(x) inside C[x] decompose the fraction F=(1/P)

$${find}\:{the}\:{roots}\:{of}\:{P}\left({x}\right)=\left(\mathrm{1}+{ix}\:+{jx}^{\mathrm{2}} \right)^{{n}} −\mathrm{1} \\ $$$${with}\:{j}\:={e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{3}}} \:\:\:{then}\:{factorize}\:{P}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$${decompose}\:{the}\:{fraction}\:{F}=\frac{\mathrm{1}}{{P}} \\ $$

Question Number 73484 Answers: 1 Comments: 0

decompose inside C(x) the fraction F(x)=(1/((x^2 +1)^n )) calculate ∫_0 ^∞ F(x)dx

$${decompose}\:{inside}\:{C}\left({x}\right)\:{the}\:{fraction} \\ $$$${F}\left({x}\right)=\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{{n}} } \\ $$$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:{F}\left({x}\right){dx} \\ $$

Question Number 73483 Answers: 1 Comments: 0

find ∫ (dx/(x+2−(√(x^2 −x +7))))

$${find}\:\int\:\:\:\:\frac{{dx}}{{x}+\mathrm{2}−\sqrt{{x}^{\mathrm{2}} −{x}\:+\mathrm{7}}} \\ $$

Question Number 73482 Answers: 1 Comments: 1

find ∫ (dx/((√(x^2 +1))+(√(x^2 +3))))

$${find}\:\int\:\:\:\:\frac{{dx}}{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}+\sqrt{{x}^{\mathrm{2}} \:+\mathrm{3}}} \\ $$

Question Number 73481 Answers: 0 Comments: 0

find ∫ ln(x−cosx)dx

$${find}\:\int\:\:{ln}\left({x}−{cosx}\right){dx} \\ $$

Question Number 73480 Answers: 0 Comments: 0

find ∫_0 ^∞ xe^(−x^2 ) arcran(x+(1/x))dx

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

Question Number 73479 Answers: 1 Comments: 1

find ∫ ((3x+2)/((x+1)^2 (x−2)^3 ))dx

$${find}\:\int\:\:\:\:\frac{\mathrm{3}{x}+\mathrm{2}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} \left({x}−\mathrm{2}\right)^{\mathrm{3}} }{dx} \\ $$

Question Number 73478 Answers: 1 Comments: 0

find ∫_0 ^1 ((x^3 −3)/(√(x^2 −x +2)))dx

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\:\frac{{x}^{\mathrm{3}} −\mathrm{3}}{\sqrt{{x}^{\mathrm{2}} −{x}\:+\mathrm{2}}}{dx} \\ $$

Question Number 73477 Answers: 1 Comments: 0

calculate ∫ ((x^3 −4x+5)/(x^2 −x +1))dx

$${calculate}\:\int\:\:\:\frac{{x}^{\mathrm{3}} −\mathrm{4}{x}+\mathrm{5}}{{x}^{\mathrm{2}} −{x}\:+\mathrm{1}}{dx} \\ $$

Question Number 73474 Answers: 0 Comments: 0

⌉888>>>>>>>

$$\rceil\mathrm{888}>>>>>>> \\ $$

Question Number 73473 Answers: 0 Comments: 1

let z from C prove that arcsinz=−iln(iz+(√(1−z^2 ))) arccosz =−iln(z+(√(z^2 −1)))

$${let}\:{z}\:{from}\:{C}\:{prove}\:{that}\: \\ $$$${arcsinz}=−{iln}\left({iz}+\sqrt{\mathrm{1}−{z}^{\mathrm{2}} }\right) \\ $$$${arccosz}\:=−{iln}\left({z}+\sqrt{{z}^{\mathrm{2}} −\mathrm{1}}\right) \\ $$

Question Number 73468 Answers: 1 Comments: 0

soit le systeme suivant { ((2s+4c+3t=700)),((3s+2c+2t=500)) :} 8s+7c+8t=...?... comment determiner le resultat ...?... de la 3^e equation ?

$$\mathrm{soit}\:\mathrm{le}\:\mathrm{systeme}\:\mathrm{suivant} \\ $$$$\begin{cases}{\mathrm{2s}+\mathrm{4c}+\mathrm{3t}=\mathrm{700}}\\{\mathrm{3s}+\mathrm{2c}+\mathrm{2t}=\mathrm{500}}\end{cases} \\ $$$$\:\:\mathrm{8s}+\mathrm{7c}+\mathrm{8t}=...?... \\ $$$$\mathrm{comment}\:\mathrm{determiner}\:\mathrm{le}\:\mathrm{resultat}\:...?...\: \\ $$$$\mathrm{de}\:\mathrm{la}\:\mathrm{3}^{\mathrm{e}} \mathrm{equation}\:? \\ $$

Question Number 73466 Answers: 1 Comments: 0

please explain this Lim_(x→0) ((sinx)/x) = 1 by l′hopitals theorem Lim_(x→0) ((sinx)/x) = 0 by Squeez theorem is there something wrong?

$${please}\:{explain}\:{this}\: \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}} {{Lim}}\frac{{sinx}}{{x}}\:=\:\mathrm{1}\:\:{by}\:{l}'{hopitals}\:{theorem} \\ $$$$ \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {{Lim}}\:\frac{{sinx}}{{x}}\:=\:\mathrm{0}\:{by}\:{Squeez}\:{theorem} \\ $$$${is}\:{there}\:{something}\:{wrong}? \\ $$

Question Number 73451 Answers: 0 Comments: 3

Question Number 73441 Answers: 1 Comments: 0

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