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Question Number 90952 Answers: 1 Comments: 0

solve diff equation x^2 y′′ + xy′ +y = 5x^2 x >0

$$ \\ $$$${solve}\:{diff}\:{equation}\: \\ $$$${x}^{\mathrm{2}} {y}''\:+\:{xy}'\:+{y}\:=\:\mathrm{5}{x}^{\mathrm{2}} \:\:{x}\:>\mathrm{0} \\ $$

Question Number 90948 Answers: 2 Comments: 2

Question Number 90947 Answers: 0 Comments: 0

if α^(13) =1 and α≠1,find the quadratic equation whose roots are (α+α^3 +α^4 +α^(−4) +α^(−3) +α^(−1) ) and (α^2 +α^5 +α^6 +α^(−6) +α^(−5) +α^(−6) )

$${if}\:\alpha^{\mathrm{13}} =\mathrm{1}\:{and}\:\alpha\neq\mathrm{1},{find}\:{the}\:{quadratic}\:\:{equation} \\ $$$${whose}\:{roots}\:{are}\:\left(\alpha+\alpha^{\mathrm{3}} +\alpha^{\mathrm{4}} +\alpha^{−\mathrm{4}} +\alpha^{−\mathrm{3}} +\alpha^{−\mathrm{1}} \right)\:{and}\:\left(\alpha^{\mathrm{2}} +\alpha^{\mathrm{5}} +\alpha^{\mathrm{6}} +\alpha^{−\mathrm{6}} +\alpha^{−\mathrm{5}} +\alpha^{−\mathrm{6}} \right) \\ $$

Question Number 90946 Answers: 0 Comments: 0

determine x,y,z ∈ R such that 2x^2 +y^2 +2z^2 −8x+2y−2xy+2xz−16z+35=0

$${determine}\:{x},{y},{z}\:\in\:\mathbb{R}\:{such}\:{that}\: \\ $$$$\mathrm{2}{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{2}{z}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{2}{y}−\mathrm{2}{xy}+\mathrm{2}{xz}−\mathrm{16}{z}+\mathrm{35}=\mathrm{0} \\ $$

Question Number 90944 Answers: 0 Comments: 3

lim_(x→0) ((x sin x)/(2sin^2 3x−x^2 cos x)) ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\:\mathrm{sin}\:{x}}{\mathrm{2sin}\:^{\mathrm{2}} \mathrm{3}{x}−{x}^{\mathrm{2}} \:\mathrm{cos}\:{x}}\:? \\ $$

Question Number 90940 Answers: 1 Comments: 0

f(x)=(x)^(1/3) is there an inflection point when x=0

$${f}\left({x}\right)=\sqrt[{\mathrm{3}}]{{x}}\:\:{is}\:{there}\:{an}\:{inflection}\:{point} \\ $$$${when}\:{x}=\mathrm{0} \\ $$

Question Number 90938 Answers: 0 Comments: 0

∫(dx/(sin(x)+cos(x)+tan(x)+cot(x)+sec(x)+csc(x)))

$$\int\frac{{dx}}{{sin}\left({x}\right)+{cos}\left({x}\right)+{tan}\left({x}\right)+{cot}\left({x}\right)+{sec}\left({x}\right)+{csc}\left({x}\right)} \\ $$

Question Number 90923 Answers: 1 Comments: 1

Question Number 90918 Answers: 0 Comments: 1

do you all get notifications when your posts get updated? i don′t get any notification. so i don′t know if a post of mine is updated or not, very uncomfortable.

$${do}\:{you}\:{all}\:{get}\:{notifications}\:{when} \\ $$$${your}\:{posts}\:{get}\:{updated}? \\ $$$${i}\:{don}'{t}\:{get}\:{any}\:{notification}.\:{so}\:{i}\:{don}'{t} \\ $$$${know}\:{if}\:{a}\:{post}\:{of}\:{mine}\:{is}\:{updated}\:{or} \\ $$$${not},\:{very}\:{uncomfortable}. \\ $$

Question Number 90916 Answers: 0 Comments: 0

Question Number 90914 Answers: 0 Comments: 2

Question Number 90911 Answers: 0 Comments: 3

Question Number 90886 Answers: 1 Comments: 0

(dy/dx) −((4y)/x) = 1+(2/x)

$$\frac{{dy}}{{dx}}\:−\frac{\mathrm{4}{y}}{{x}}\:=\:\mathrm{1}+\frac{\mathrm{2}}{{x}} \\ $$

Question Number 90881 Answers: 2 Comments: 6

if the value of x is in degrees what is the derivative of f(x)=sin(x)

$${if}\:{the}\:{value}\:{of}\:{x}\:{is}\:{in}\:{degrees}\:{what}\:{is} \\ $$$${the}\:{derivative}\:{of}\:\:\:{f}\left({x}\right)={sin}\left({x}\right) \\ $$

Question Number 90876 Answers: 0 Comments: 2

((2cos ((π/9))))^(1/(3 )) −((2cos (((2π)/9))))^(1/(3 )) −((2cos (((4π)/9))))^(1/(3 )) = ?

$$\sqrt[{\mathrm{3}\:\:}]{\mathrm{2cos}\:\left(\frac{\pi}{\mathrm{9}}\right)}−\sqrt[{\mathrm{3}\:\:}]{\mathrm{2cos}\:\left(\frac{\mathrm{2}\pi}{\mathrm{9}}\right)}−\sqrt[{\mathrm{3}\:\:}]{\mathrm{2cos}\:\left(\frac{\mathrm{4}\pi}{\mathrm{9}}\right)}\:=\:? \\ $$

Question Number 90904 Answers: 1 Comments: 1

Question Number 90851 Answers: 1 Comments: 0

x (dy/dx) = y + 3x^4 cos^2 ((y/x))

$${x}\:\frac{{dy}}{{dx}}\:=\:{y}\:+\:\mathrm{3}{x}^{\mathrm{4}} \:\mathrm{cos}\:^{\mathrm{2}} \left(\frac{{y}}{{x}}\right)\: \\ $$

Question Number 90842 Answers: 3 Comments: 4

x^2 −(y−z)^2 = 3 y^2 − (z−x)^2 = 5 z^2 − (x−y)^2 = 12

$${x}^{\mathrm{2}} −\left({y}−{z}\right)^{\mathrm{2}} \:=\:\mathrm{3} \\ $$$${y}^{\mathrm{2}} \:−\:\left({z}−{x}\right)^{\mathrm{2}} \:=\:\mathrm{5} \\ $$$${z}^{\mathrm{2}} \:−\:\left({x}−{y}\right)^{\mathrm{2}} \:=\:\mathrm{12} \\ $$

Question Number 90863 Answers: 2 Comments: 0

(dy/dx)−a((y/x))=1+(1/x)

$$\frac{{dy}}{{dx}}−{a}\left(\frac{{y}}{{x}}\right)=\mathrm{1}+\frac{\mathrm{1}}{{x}} \\ $$

Question Number 91004 Answers: 0 Comments: 3

∫ tan (arc sin x) dx

$$\int\:\mathrm{tan}\:\left({arc}\:\mathrm{sin}\:{x}\right)\:{dx} \\ $$

Question Number 90819 Answers: 2 Comments: 2

Question Number 90812 Answers: 0 Comments: 0

Question Number 90810 Answers: 1 Comments: 2

(dy/dx) = ((2x^2 +y^2 )/(3x^2 +2xy))

$$\frac{{dy}}{{dx}}\:=\:\frac{\mathrm{2}{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}{xy}}\: \\ $$

Question Number 90806 Answers: 0 Comments: 1

log_((x+4)) (x^2 −8x+12) < (1/2)log_(∣x−2∣) (2−x)^2

$$\mathrm{log}_{\left({x}+\mathrm{4}\right)} \left({x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{12}\right)\:<\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{log}_{\mid{x}−\mathrm{2}\mid} \left(\mathrm{2}−{x}\right)^{\mathrm{2}} \\ $$

Question Number 90803 Answers: 0 Comments: 0

U=ax−bx^c +dy is subject to I=mx+ny. What happens to the maximum point of x, when a increases? Explain your answer. (Use Lagrange method)

$${U}={ax}−{bx}^{{c}} +{dy}\:\mathrm{is}\:\mathrm{subject}\:\mathrm{to}\:\mathrm{I}={mx}+{ny}. \\ $$$$ \\ $$$$\mathrm{What}\:\mathrm{happens}\:\mathrm{to}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{point}\:\mathrm{of}\:\boldsymbol{{x}}, \\ $$$${when}\:\boldsymbol{{a}}\:\mathrm{increases}?\:\mathrm{Explain}\:\mathrm{your}\:\mathrm{answer}. \\ $$$$ \\ $$$$\left(\mathrm{Use}\:\mathrm{Lagrange}\:\mathrm{method}\right) \\ $$

Question Number 90802 Answers: 0 Comments: 2

1) ∫_(ln 2) ^∞ (1/(√(e^x −1))) dx 2) ∫_(ln 2) ^∞ (1/(e^x −1)) dx

$$\left.\mathrm{1}\right)\:\underset{\mathrm{ln}\:\mathrm{2}} {\overset{\infty} {\int}}\:\frac{\mathrm{1}}{\sqrt{\mathrm{e}^{{x}} −\mathrm{1}}}\:{dx}\: \\ $$$$\left.\mathrm{2}\right)\:\underset{\mathrm{ln}\:\mathrm{2}} {\overset{\infty} {\int}}\:\frac{\mathrm{1}}{{e}^{{x}} −\mathrm{1}}\:{dx}\: \\ $$

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