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AllQuestion and Answers: Page 1265

Question Number 82339 Answers: 0 Comments: 1

Question Number 82658 Answers: 1 Comments: 2

coefficient x^6 from expressi (2x+1)^(6 ) × (x^2 +x+(1/4))^4 ?

$${coefficient}\:{x}^{\mathrm{6}} \:{from}\:{expressi}\: \\ $$$$\left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{6}\:} ×\:\left({x}^{\mathrm{2}} +{x}+\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{4}} \:? \\ $$

Question Number 82333 Answers: 0 Comments: 0

(y^4 −2xy) dx = −3x^2 dy

$$\left({y}^{\mathrm{4}} −\mathrm{2}{xy}\right)\:{dx}\:=\:−\mathrm{3}{x}^{\mathrm{2}} \:{dy} \\ $$

Question Number 82330 Answers: 0 Comments: 4

Question Number 82308 Answers: 0 Comments: 1

Question Number 82307 Answers: 0 Comments: 3

Question Number 82303 Answers: 0 Comments: 18

Question Number 82302 Answers: 0 Comments: 2

Question Number 82290 Answers: 0 Comments: 0

calculate Σ_(p≥2 and q≥2) (1/p^q )

$${calculate}\:\sum_{{p}\geqslant\mathrm{2}\:{and}\:{q}\geqslant\mathrm{2}} \:\:\frac{\mathrm{1}}{{p}^{{q}} } \\ $$

Question Number 82289 Answers: 1 Comments: 4

calculate Σ_(n=6) ^∞ (1/(n^2 −25))

$${calculate}\:\sum_{{n}=\mathrm{6}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} −\mathrm{25}} \\ $$

Question Number 82288 Answers: 0 Comments: 0

calculate lim_(n→+∞) (1+(1/n))^n^2 ((n!)/n^(n+(1/2)) )

$${calculate}\:{lim}_{{n}\rightarrow+\infty} \left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}^{\mathrm{2}} } \frac{{n}!}{{n}^{{n}+\frac{\mathrm{1}}{\mathrm{2}}} } \\ $$

Question Number 82287 Answers: 0 Comments: 0

find nature of the serie Σ (n^n /(n! e^n ))

$${find}\:{nature}\:{of}\:{the}\:{serie}\:\Sigma\:\frac{{n}^{{n}} }{{n}!\:{e}^{{n}} } \\ $$

Question Number 82286 Answers: 1 Comments: 3

1) find a and b wich verify ∫_0 ^π (at^2 +bt)cos(nx) =(1/n^2 ) 2) find the value of Σ_(n=1) ^∞ (1/n^2 )

$$\left.\mathrm{1}\right)\:{find}\:{a}\:{and}\:{b}\:{wich}\:{verify}\:\:\int_{\mathrm{0}} ^{\pi} \left({at}^{\mathrm{2}} \:+{bt}\right){cos}\left({nx}\right)\:=\frac{\mathrm{1}}{{n}^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{2}} } \\ $$

Question Number 82285 Answers: 0 Comments: 0

Question Number 82284 Answers: 0 Comments: 0

Question Number 82283 Answers: 1 Comments: 2

∫x^3 (√(x^3 +1)) dx

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

Question Number 82279 Answers: 0 Comments: 0

Question Number 82277 Answers: 0 Comments: 4

Question Number 82276 Answers: 0 Comments: 0

Question Number 82274 Answers: 0 Comments: 0

Question Number 82273 Answers: 0 Comments: 2

Question Number 82390 Answers: 1 Comments: 0

(D^2 −1)^2 y = t^3 find solution

$$\left({D}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} {y}\:=\:{t}^{\mathrm{3}} \\ $$$${find}\:{solution} \\ $$

Question Number 82265 Answers: 2 Comments: 0

factorize: (x+1)(x+2)(x+3)(x+6)−3x^2

$${f}\boldsymbol{{actorize}}: \\ $$$$\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)\left({x}+\mathrm{6}\right)−\mathrm{3}{x}^{\mathrm{2}} \\ $$$$ \\ $$

Question Number 82247 Answers: 1 Comments: 1

(D^4 +2D^2 +1)y =x^2 cos x

$$\left({D}^{\mathrm{4}} +\mathrm{2}{D}^{\mathrm{2}} +\mathrm{1}\right){y}\:={x}^{\mathrm{2}} \:\mathrm{cos}\:{x}\: \\ $$

Question Number 82245 Answers: 0 Comments: 2

find the solution x sin ((y/x)) dy = [y sin ((y/x)) −x] dx

$${find}\:{the}\:{solution}\: \\ $$$${x}\:\mathrm{sin}\:\left(\frac{{y}}{{x}}\right)\:{dy}\:=\:\left[{y}\:\mathrm{sin}\:\left(\frac{{y}}{{x}}\right)\:−{x}\right]\:{dx} \\ $$

Question Number 82244 Answers: 1 Comments: 2

find the function of f when this function continue at interval [−∞,0] ∫_(−x^2 ) ^0 f(t) dt=(d/dx)[x(1−sin(πx)]

$${find}\:{the}\:{function}\:{of}\:{f}\:{when}\:{this}\:\: \\ $$$${function}\:{continue}\:{at}\:{interval}\:\left[−\infty,\mathrm{0}\right] \\ $$$$\int_{−{x}^{\mathrm{2}} } ^{\mathrm{0}} {f}\left({t}\right)\:{dt}=\frac{{d}}{{dx}}\left[{x}\left(\mathrm{1}−{sin}\left(\pi{x}\right)\right]\right. \\ $$

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