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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)]

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

Question Number 82243 Answers: 1 Comments: 0

Question Number 82232 Answers: 1 Comments: 1

Question Number 82223 Answers: 0 Comments: 1

given f(x) = f(x+(π/6)) , ∀x∈ R if ∫_0 ^(π/6) f(x) dx = T then ∫_π ^((7π)/3) f(x+π) dx = ?

$${given}\:{f}\left({x}\right)\:=\:{f}\left({x}+\frac{\pi}{\mathrm{6}}\right)\:,\:\forall{x}\in\:\mathbb{R} \\ $$$${if}\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{6}}} {\int}}\:{f}\left({x}\right)\:{dx}\:=\:{T}\: \\ $$$${then}\:\underset{\pi} {\overset{\frac{\mathrm{7}\pi}{\mathrm{3}}} {\int}}\:{f}\left({x}+\pi\right)\:{dx}\:=\:? \\ $$

Question Number 82225 Answers: 0 Comments: 3

Question Number 82191 Answers: 1 Comments: 19

find the solution (√(x^2 −3x−4 )) > x−2

$${find}\:{the}\:{solution} \\ $$$$\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{4}\:}\:\:>\:\:{x}−\mathrm{2}\: \\ $$

Question Number 82185 Answers: 1 Comments: 2

∫ (dx/(sec x + csc x)) = ?

$$\int\:\frac{{dx}}{\mathrm{sec}\:{x}\:+\:{csc}\:{x}}\:=\:?\: \\ $$

Question Number 82176 Answers: 0 Comments: 3

Question Number 82175 Answers: 1 Comments: 4

lim_(x→−∞) ((8x^3 −4x^2 +1))^(1/(3 )) −((8x^3 +∣px∣^2 −1))^(1/(3 )) = (1/4) find p

$$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\sqrt[{\mathrm{3}\:}]{\mathrm{8}{x}^{\mathrm{3}} −\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}}−\sqrt[{\mathrm{3}\:}]{\mathrm{8}{x}^{\mathrm{3}} +\mid{px}\mid^{\mathrm{2}} −\mathrm{1}}\:=\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$${find}\:{p}\: \\ $$

Question Number 82174 Answers: 1 Comments: 1

∫_0 ^π x ln(sin x) dx = ?

$$\underset{\mathrm{0}} {\overset{\pi} {\int}}\:{x}\:{ln}\left(\mathrm{sin}\:{x}\right)\:{dx}\:=\:?\: \\ $$

Question Number 82160 Answers: 2 Comments: 0

prove that lim_(x→∞) n^2 (√((1−cos((1/n))(√((1−cos(1/n))(√((1−cos(1/n))...)))))) =(1/2)

$${prove}\:{that} \\ $$$$\underset{{x}\rightarrow\infty} {{lim}}\:{n}^{\mathrm{2}} \:\sqrt{\left(\mathrm{1}−{cos}\left(\frac{\mathrm{1}}{{n}}\right)\sqrt{\left(\mathrm{1}−{cos}\frac{\mathrm{1}}{{n}}\right)\sqrt{\left(\mathrm{1}−{cos}\frac{\mathrm{1}}{{n}}\right)...}}\right.}\:=\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 82149 Answers: 1 Comments: 1

Evaluate the greatest coefficient of (7 − 5x)^(− 3)

$$\mathrm{Evaluate}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{coefficient}\:\mathrm{of}\:\:\:\:\left(\mathrm{7}\:−\:\mathrm{5x}\right)^{−\:\mathrm{3}} \\ $$

Question Number 82139 Answers: 1 Comments: 0

∫ ((√(x^4 +x^(−4) +2))/x^3 ) dx

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

Question Number 82138 Answers: 0 Comments: 1

Question Number 82134 Answers: 0 Comments: 6

Question Number 82131 Answers: 2 Comments: 4

Question Number 82125 Answers: 0 Comments: 5

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