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Question Number 92474    Answers: 0   Comments: 0

please anyone wanna help me with Q91948

$$\mathrm{please}\:\mathrm{anyone}\:\mathrm{wanna}\:\mathrm{help}\:\mathrm{me}\:\mathrm{with}\:\mathrm{Q91948} \\ $$

Question Number 92468    Answers: 1   Comments: 0

y (d^2 y/dx)−9y = 3

$$\mathrm{y}\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}}−\mathrm{9y}\:=\:\mathrm{3} \\ $$

Question Number 92465    Answers: 1   Comments: 7

for a 2d vectors if ∣a + b∣ = ∣a−b∣ what relationship does a and b have?

$$\mathrm{for}\:\mathrm{a}\:\mathrm{2d}\:\:\mathrm{vectors}\:\mathrm{if}\:\mid{a}\:+\:{b}\mid\:=\:\mid{a}−{b}\mid\:\mathrm{what}\:\mathrm{relationship}\:\mathrm{does}\:{a}\:\mathrm{and}\:{b}\:\mathrm{have}? \\ $$$$ \\ $$

Question Number 92464    Answers: 0   Comments: 4

(dy/dx) = (e^y /x^2 ) − (1/x)

$$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{e}^{\mathrm{y}} }{\mathrm{x}^{\mathrm{2}} }\:−\:\frac{\mathrm{1}}{\mathrm{x}} \\ $$

Question Number 92461    Answers: 0   Comments: 1

cos (((3x)/4)−π)=sin ((π/4)−2x) x ∈ [0, π ]

$$\mathrm{cos}\:\left(\frac{\mathrm{3x}}{\mathrm{4}}−\pi\right)=\mathrm{sin}\:\left(\frac{\pi}{\mathrm{4}}−\mathrm{2x}\right) \\ $$$$\mathrm{x}\:\in\:\left[\mathrm{0},\:\pi\:\right]\: \\ $$

Question Number 92453    Answers: 0   Comments: 2

(( i))^(1/(i )) ?

$$\sqrt[{\mathrm{i}\:\:}]{\:\mathrm{i}}\:? \\ $$

Question Number 92452    Answers: 0   Comments: 0

(2xy^2 −y)dx = (2x−x^2 y)dy

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

Question Number 92448    Answers: 4   Comments: 1

{ ((5^x .6^y = 150)),((5^y .6^x = 180 )) :}

$$\begin{cases}{\mathrm{5}^{\mathrm{x}} .\mathrm{6}^{\mathrm{y}} \:=\:\mathrm{150}}\\{\mathrm{5}^{\mathrm{y}} .\mathrm{6}^{\mathrm{x}} \:=\:\mathrm{180}\:}\end{cases} \\ $$

Question Number 92445    Answers: 1   Comments: 0

Question Number 92438    Answers: 0   Comments: 1

find the domaine and simplify the function f(x)=arcos(((1−x^2 )/(1+x^2 )))

$$\mathrm{find}\:\mathrm{the}\:\mathrm{domaine}\:\mathrm{and}\:\mathrm{simplify} \\ $$$$\mathrm{the}\:\mathrm{function} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{arcos}\left(\frac{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\right) \\ $$

Question Number 92426    Answers: 0   Comments: 4

If x^2 +2xy=0 find y

$$\mathrm{If}\:\mathrm{x}^{\mathrm{2}} +\mathrm{2xy}=\mathrm{0}\:\mathrm{find}\:\mathrm{y} \\ $$

Question Number 92425    Answers: 0   Comments: 1

If A and B are two different number such that A+B=C and A×B=C find A and B.

$$\mathrm{If}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{two} \\ $$$$\mathrm{different}\:\mathrm{number}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{A}+\mathrm{B}=\mathrm{C}\:\mathrm{and}\:\mathrm{A}×\mathrm{B}=\mathrm{C} \\ $$$$\mathrm{find}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}. \\ $$

Question Number 92424    Answers: 0   Comments: 3

If 2x−0i=ϱ^(πi) find the value of x

$$\mathrm{If}\:\mathrm{2x}−\mathrm{0i}=\varrho^{\pi\mathrm{i}} \: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$

Question Number 92423    Answers: 1   Comments: 0

lim_(x⇒∞) ((4(x+3)!−x!)/(x[(x+2)!−(x−1)!]))

$${lim}_{{x}\Rightarrow\infty} \frac{\mathrm{4}\left({x}+\mathrm{3}\right)!−{x}!}{{x}\left[\left({x}+\mathrm{2}\right)!−\left({x}−\mathrm{1}\right)!\right]} \\ $$

Question Number 92422    Answers: 0   Comments: 0

solve (y^2 +yz)dx+(z^2 +xy)dy+(y^2 −xy)dz=0 help me sir

$${solve}\:\left({y}^{\mathrm{2}} +{yz}\right){dx}+\left({z}^{\mathrm{2}} +{xy}\right){dy}+\left({y}^{\mathrm{2}} −{xy}\right){dz}=\mathrm{0} \\ $$$$ \\ $$$${help}\:{me}\:{sir} \\ $$

Question Number 92421    Answers: 1   Comments: 0

∫((cscx)/(cos(2x)+2cos^2 x))dx pleas sir help me

$$\int\frac{{cscx}}{{cos}\left(\mathrm{2}{x}\right)+\mathrm{2}{cos}^{\mathrm{2}} {x}}{dx} \\ $$$${pleas}\:{sir}\:{help}\:{me} \\ $$

Question Number 92420    Answers: 2   Comments: 2

Question Number 92447    Answers: 0   Comments: 1

find ∫_(1/6) ^(1/5) (dx/((√(1−3x))+(√(1+3x))))

$${find}\:\int_{\frac{\mathrm{1}}{\mathrm{6}}} ^{\frac{\mathrm{1}}{\mathrm{5}}} \:\:\frac{{dx}}{\sqrt{\mathrm{1}−\mathrm{3}{x}}+\sqrt{\mathrm{1}+\mathrm{3}{x}}} \\ $$

Question Number 92410    Answers: 0   Comments: 3

find ∫_1 ^(√2) (dx/((√(1+3x))−(√(1−3x))))

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

Question Number 92407    Answers: 0   Comments: 0

let f(a) =∫_0 ^1 ln((√(1+x))+a(√(1−x)))dx with a>0 1)explicite f(a) 2)find g(a) =∫_0 ^1 ((√(1−x))/((√(1+x))+a(√(1−x)))) dx 3) find the value of ∫_0 ^1 ln((√(1+x))+2(√(1−x)))dx and ∫_0 ^1 ln((√(1+x))+(1/3)(√(1−x)))dx 4) calculate A(θ) =∫_0 ^1 ln((√(1+x))+sinθ (√(1−x)))dx 0<θ<(π/2)

$${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\sqrt{\mathrm{1}+{x}}+{a}\sqrt{\mathrm{1}−{x}}\right){dx}\:\:\:{with}\:\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right){explicite}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{g}\left({a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\sqrt{\mathrm{1}−{x}}}{\sqrt{\mathrm{1}+{x}}+{a}\sqrt{\mathrm{1}−{x}}}\:{dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\sqrt{\mathrm{1}+{x}}+\mathrm{2}\sqrt{\mathrm{1}−{x}}\right){dx} \\ $$$${and}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\sqrt{\mathrm{1}+{x}}+\frac{\mathrm{1}}{\mathrm{3}}\sqrt{\mathrm{1}−{x}}\right){dx} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:{A}\left(\theta\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\sqrt{\mathrm{1}+{x}}+{sin}\theta\:\sqrt{\mathrm{1}−{x}}\right){dx}\: \\ $$$$\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}} \\ $$

Question Number 92399    Answers: 0   Comments: 1

sin^3 (x)+cos^4 (x) = 0

$$\mathrm{sin}\:^{\mathrm{3}} \left(\mathrm{x}\right)+\mathrm{cos}\:^{\mathrm{4}} \left(\mathrm{x}\right)\:=\:\mathrm{0} \\ $$

Question Number 92398    Answers: 1   Comments: 0

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

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

Question Number 92397    Answers: 0   Comments: 2

∫ (1/(x−(√(1−x^2 )))) dx [ x = sin w ] ∫ ((cos w dw)/(sin w−cos w)) = ∫ (dw/(tan w−1)) = ∫ ((sec^2 w dw)/((tan w−1)sec^2 w)) = ∫ (du/((u−1)(u^2 +1))) ; [ u = tan w ] = ∫ (du/(2(u−1)))−∫ ((u du )/(2(u^2 +1))) = (1/2)ln ∣u−1∣ −(1/4)ln∣u^2 +1∣ −(1/2)tan^(−1) (u) +c = (1/2)ln∣tan w−1∣−(1/4)ln∣tan^2 w+1∣− (1/2) tan^(−1) (tan w) +c = (1/2)ln∣(x/(√(1−x^2 )))−1∣+(1/4)ln∣1−x^2 ∣− (1/2)sin^(−1) (x) + c

$$\int\:\frac{\mathrm{1}}{{x}−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:{dx}\: \\ $$$$\left[\:{x}\:=\:\mathrm{sin}\:{w}\:\right]\: \\ $$$$\int\:\frac{\mathrm{cos}\:\mathrm{w}\:\mathrm{dw}}{\mathrm{sin}\:\mathrm{w}−\mathrm{cos}\:\mathrm{w}}\:=\:\int\:\frac{\mathrm{dw}}{\mathrm{tan}\:\mathrm{w}−\mathrm{1}} \\ $$$$=\:\int\:\frac{\mathrm{sec}^{\mathrm{2}} \:\mathrm{w}\:\mathrm{dw}}{\left(\mathrm{tan}\:\mathrm{w}−\mathrm{1}\right)\mathrm{sec}^{\mathrm{2}} \:\mathrm{w}} \\ $$$$=\:\int\:\frac{\mathrm{du}}{\left(\mathrm{u}−\mathrm{1}\right)\left(\mathrm{u}^{\mathrm{2}} +\mathrm{1}\right)}\:;\:\left[\:\mathrm{u}\:=\:\mathrm{tan}\:\mathrm{w}\:\right]\: \\ $$$$=\:\int\:\frac{\mathrm{du}}{\mathrm{2}\left(\mathrm{u}−\mathrm{1}\right)}−\int\:\frac{\mathrm{u}\:\mathrm{du}\:}{\mathrm{2}\left(\mathrm{u}^{\mathrm{2}} +\mathrm{1}\right)} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\mid\mathrm{u}−\mathrm{1}\mid\:−\frac{\mathrm{1}}{\mathrm{4}}\mathrm{ln}\mid\mathrm{u}^{\mathrm{2}} +\mathrm{1}\mid\:−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{u}\right)\:+\mathrm{c} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\mid\mathrm{tan}\:\mathrm{w}−\mathrm{1}\mid−\frac{\mathrm{1}}{\mathrm{4}}\mathrm{ln}\mid\mathrm{tan}\:^{\mathrm{2}} \mathrm{w}+\mathrm{1}\mid− \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{tan}\:\mathrm{w}\right)\:+\mathrm{c} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\mid\frac{{x}}{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}−\mathrm{1}\mid+\frac{\mathrm{1}}{\mathrm{4}}\mathrm{ln}\mid\mathrm{1}−{x}^{\mathrm{2}} \mid− \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}^{−\mathrm{1}} \left({x}\right)\:+\:{c} \\ $$

Question Number 92394    Answers: 0   Comments: 2

∫ ln ((√(1−x)) + (√(1+x)) ) dx

$$\int\:\mathrm{ln}\:\left(\sqrt{\mathrm{1}−{x}}\:+\:\sqrt{\mathrm{1}+{x}}\:\right)\:{dx}\: \\ $$

Question Number 92390    Answers: 0   Comments: 2

What is the meaning of this symbol (ε) in limit please. or as used in convergent/divergent series

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{meaning}\:\mathrm{of}\:\mathrm{this}\:\mathrm{symbol}\:\:\left(\varepsilon\right)\:\mathrm{in}\:\mathrm{limit}\:\mathrm{please}. \\ $$$$\mathrm{or}\:\mathrm{as}\:\mathrm{used}\:\mathrm{in}\:\mathrm{convergent}/\mathrm{divergent}\:\mathrm{series} \\ $$

Question Number 92366    Answers: 0   Comments: 3

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