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Question Number 96194 Answers: 2 Comments: 0

let f(x) =ln(cosx) developp f at fourier serie

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{ln}\left(\mathrm{cosx}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 96193 Answers: 0 Comments: 0

calculate ∫_0 ^(π/2) (ln(cosx))^2 dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left(\mathrm{ln}\left(\mathrm{cosx}\right)\right)^{\mathrm{2}} \:\mathrm{dx} \\ $$

Question Number 96192 Answers: 0 Comments: 2

find a particular solution to the equation y′ =(y/x)+sin(y/x) with original condition y(1)=(π/2)

$$\mathrm{find}\:\mathrm{a}\:\mathrm{particular}\:\mathrm{solution}\:\mathrm{to}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{y}'\:=\frac{\mathrm{y}}{\mathrm{x}}+\mathrm{sin}\frac{\mathrm{y}}{\mathrm{x}}\:\mathrm{with}\:\mathrm{original}\:\mathrm{condition} \\ $$$$\mathrm{y}\left(\mathrm{1}\right)=\frac{\pi}{\mathrm{2}} \\ $$

Question Number 96189 Answers: 3 Comments: 0

find a common roots from the two quadratic eq 24x^2 +(p+4)x−1=0 and 6x^2 +11x+p+2=0

$$\mathrm{find}\:\mathrm{a}\:\mathrm{common}\:\mathrm{roots}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{two}\:\mathrm{quadratic}\:\mathrm{eq} \\ $$$$\mathrm{24x}^{\mathrm{2}} +\left(\mathrm{p}+\mathrm{4}\right)\mathrm{x}−\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{and}\:\mathrm{6x}^{\mathrm{2}} +\mathrm{11x}+\mathrm{p}+\mathrm{2}=\mathrm{0} \\ $$

Question Number 96185 Answers: 1 Comments: 0

what are critical points of this function z = xy+5xy^2 +10y

$$\mathrm{what}\:\mathrm{are}\:\mathrm{critical}\:\mathrm{points}\:\mathrm{of}\:\mathrm{this} \\ $$$$\mathrm{function}\:\mathrm{z}\:=\:\mathrm{xy}+\mathrm{5xy}^{\mathrm{2}} +\mathrm{10y} \\ $$

Question Number 96182 Answers: 1 Comments: 0

x^2 y′′−xy′+y = 0

$${x}^{\mathrm{2}} {y}''−{xy}'+\mathrm{y}\:=\:\mathrm{0}\: \\ $$

Question Number 96175 Answers: 1 Comments: 1

∫(dx/(√(4x^2 +4x+3)))=?

$$\int\frac{{dx}}{\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{3}}}=? \\ $$

Question Number 96171 Answers: 0 Comments: 2

(4+(√(15)))^(3/2) −(4−(√(15)))^(3/2) = k(√6) find k

$$\left(\mathrm{4}+\sqrt{\mathrm{15}}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} −\left(\mathrm{4}−\sqrt{\mathrm{15}}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} =\:\mathrm{k}\sqrt{\mathrm{6}} \\ $$$$\mathrm{find}\:\mathrm{k}\: \\ $$

Question Number 96161 Answers: 1 Comments: 1

∫_1 ^4 ((sech^2 ((√x))+tanh ((√x)))/((√x) )) dx ?

$$\underset{\mathrm{1}} {\overset{\mathrm{4}} {\int}}\:\frac{\mathrm{sech}\:^{\mathrm{2}} \left(\sqrt{{x}}\right)+\mathrm{tanh}\:\left(\sqrt{{x}}\right)}{\sqrt{{x}}\:}\:{dx}\:? \\ $$

Question Number 96155 Answers: 1 Comments: 4

Question Number 96148 Answers: 2 Comments: 14

Question Number 96140 Answers: 1 Comments: 5

xy′+y^2 =x^2 e^x ⇒ y′=xe^x −(y^2 /x) ⇒ y=xye^x −(1/(3x))∙y^3 ⇒ (y^3 /(3x))+y−xye^x =0 y((y^2 /(3x))+1−xe^x )=0 ⇒ y=±(√(3x(xe^x −1)))

$$\boldsymbol{{xy}}'+\boldsymbol{{y}}^{\mathrm{2}} =\boldsymbol{{x}}^{\mathrm{2}} \boldsymbol{{e}}^{\boldsymbol{{x}}} \:\Rightarrow\:\boldsymbol{{y}}'=\boldsymbol{{xe}}^{\boldsymbol{{x}}} −\frac{\boldsymbol{{y}}^{\mathrm{2}} }{\boldsymbol{{x}}}\:\Rightarrow \\ $$$$\boldsymbol{{y}}=\boldsymbol{{xye}}^{\boldsymbol{{x}}} −\frac{\mathrm{1}}{\mathrm{3}\boldsymbol{{x}}}\centerdot\boldsymbol{{y}}^{\mathrm{3}} \Rightarrow\:\frac{\boldsymbol{{y}}^{\mathrm{3}} }{\mathrm{3}\boldsymbol{{x}}}+\boldsymbol{{y}}−\boldsymbol{{xye}}^{\boldsymbol{{x}}} =\mathrm{0} \\ $$$$\boldsymbol{{y}}\left(\frac{\boldsymbol{{y}}^{\mathrm{2}} }{\mathrm{3}\boldsymbol{{x}}}+\mathrm{1}−\boldsymbol{{xe}}^{\boldsymbol{{x}}} \right)=\mathrm{0}\:\Rightarrow\:\boldsymbol{{y}}=\pm\sqrt{\mathrm{3}\boldsymbol{{x}}\left(\boldsymbol{{xe}}^{\boldsymbol{{x}}} −\mathrm{1}\right)} \\ $$

Question Number 96138 Answers: 0 Comments: 1

xy′ + y^2 = x^2 e^x

$${xy}'\:+\:{y}^{\mathrm{2}} \:=\:{x}^{\mathrm{2}} {e}^{{x}} \: \\ $$

Question Number 96135 Answers: 0 Comments: 5

Question Number 96128 Answers: 1 Comments: 0

find ∫∫_R (x+2y)^2 dxdy in R=[−1,2] ×[0,2]

$${find}\:\int\int_{{R}} \:\left({x}+\mathrm{2}{y}\right)^{\mathrm{2}} \:{dxdy}\:{in}\:{R}=\left[−\mathrm{1},\mathrm{2}\right]\:×\left[\mathrm{0},\mathrm{2}\right]\: \\ $$

Question Number 96131 Answers: 1 Comments: 0

(((x+4)^2 ))^(1/(3 )) + 4 (((x−3)^2 ))^(1/(3 )) + 5 ((x^2 +x−12))^(1/(3 )) = 0

$$\sqrt[{\mathrm{3}\:\:}]{\left({x}+\mathrm{4}\right)^{\mathrm{2}} }\:+\:\mathrm{4}\:\sqrt[{\mathrm{3}\:\:}]{\left({x}−\mathrm{3}\right)^{\mathrm{2}} }\:+\:\mathrm{5}\:\sqrt[{\mathrm{3}\:\:}]{{x}^{\mathrm{2}} +{x}−\mathrm{12}}\:=\:\mathrm{0} \\ $$

Question Number 96125 Answers: 1 Comments: 0

4x^2 y′′ +12xy′ + 3y = 0

$$\mathrm{4x}^{\mathrm{2}} \mathrm{y}''\:+\mathrm{12xy}'\:+\:\mathrm{3y}\:=\:\mathrm{0} \\ $$

Question Number 96117 Answers: 2 Comments: 0

(1−2xy) dx + (4y^3 −x^2 ) dy = 0

$$\left(\mathrm{1}−\mathrm{2}{xy}\right)\:{dx}\:+\:\left(\mathrm{4}{y}^{\mathrm{3}} −{x}^{\mathrm{2}} \right)\:{dy}\:=\:\mathrm{0}\: \\ $$

Question Number 96108 Answers: 0 Comments: 0

are the system (z,+,≤)is orderd integral domain ?

$${are}\:{the}\:{system}\:\left({z},+,\leqslant\right){is}\:{orderd}\:{integral}\:{domain}\:? \\ $$

Question Number 96106 Answers: 0 Comments: 1

Question Number 96097 Answers: 1 Comments: 0

Question Number 96092 Answers: 0 Comments: 4

find ∫(dx/(tan^(−1) (x)))

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

Question Number 97266 Answers: 2 Comments: 1

If x &y satisfy the equation x^2 +y^2 −4x−6y−1 =0 find minimum value of x+y ?

$$\mathrm{If}\:\mathrm{x}\:\&\mathrm{y}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{4x}−\mathrm{6y}−\mathrm{1}\:=\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}+\mathrm{y}\:? \\ $$

Question Number 96089 Answers: 2 Comments: 0

Question Number 96083 Answers: 1 Comments: 0

∫ ((e^x (1+sin x))/(1+cos x)) dx

$$\int\:\frac{\mathrm{e}^{\mathrm{x}} \left(\mathrm{1}+\mathrm{sin}\:\mathrm{x}\right)}{\mathrm{1}+\mathrm{cos}\:\mathrm{x}}\:\mathrm{dx}\: \\ $$

Question Number 96078 Answers: 0 Comments: 0

lim_((x,y)→(1,2)) sin (((x−1)/(y−2)))

$$\underset{\left({x},\mathrm{y}\right)\rightarrow\left(\mathrm{1},\mathrm{2}\right)} {\mathrm{lim}}\:\mathrm{sin}\:\left(\frac{\mathrm{x}−\mathrm{1}}{\mathrm{y}−\mathrm{2}}\right)\: \\ $$

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