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Question Number 89236 Answers: 1 Comments: 0

z(z^2 +3x)+3y=0 show that (∂^2 z/∂x^2 )+(∂^2 z/∂y^2 )=((2z(x−1))/((z^2 +x)^3 ))

$$\mathrm{z}\left(\mathrm{z}^{\mathrm{2}} +\mathrm{3x}\right)+\mathrm{3y}=\mathrm{0} \\ $$$$\mathrm{show}\:\mathrm{that} \\ $$$$\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{x}^{\mathrm{2}} }+\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{y}^{\mathrm{2}} }=\frac{\mathrm{2z}\left(\mathrm{x}−\mathrm{1}\right)}{\left(\mathrm{z}^{\mathrm{2}} +\mathrm{x}\right)^{\mathrm{3}} } \\ $$

Question Number 89238 Answers: 1 Comments: 1

∫_7 ^(12) x^2 (√(x−3))

$$\int_{\mathrm{7}} ^{\mathrm{12}} \mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{x}−\mathrm{3}} \\ $$

Question Number 89200 Answers: 0 Comments: 0

Question Number 89144 Answers: 0 Comments: 0

Question Number 89143 Answers: 0 Comments: 0

Question Number 89126 Answers: 0 Comments: 0

6[(√( ))

$$\mathrm{6}\left[\sqrt{\:\:}\right. \\ $$

Question Number 89093 Answers: 0 Comments: 0

Question Number 89092 Answers: 0 Comments: 2

Evaluate : lim_(n→∞) e^(−n) Σ_(k=0) ^n (n^k /(k!))

$${Evaluate}\::\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{e}^{−{n}} \:\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\frac{{n}^{{k}} }{{k}!} \\ $$

Question Number 89074 Answers: 0 Comments: 1

×^4 +×^2 =1

$$×^{\mathrm{4}} +×^{\mathrm{2}} =\mathrm{1} \\ $$

Question Number 89063 Answers: 0 Comments: 0

let f(x) = x^3 + 2x^2 + 3x + 4 find the region enclosed by f ′, f ′′ and f ′′′

$$\:\mathrm{let}\:{f}\left({x}\right)\:=\:{x}^{\mathrm{3}} \:+\:\mathrm{2}{x}^{\mathrm{2}} \:+\:\mathrm{3}{x}\:+\:\mathrm{4} \\ $$$$\:\mathrm{find}\:\mathrm{the}\:\mathrm{region}\:\mathrm{enclosed}\:\mathrm{by}\:{f}\:',\:{f}\:''\:\mathrm{and}\:{f}\:''' \\ $$

Question Number 89089 Answers: 1 Comments: 0

16^(3/4) +2

$$\mathrm{16}^{\mathrm{3}/\mathrm{4}} \:+\mathrm{2} \\ $$

Question Number 89038 Answers: 1 Comments: 0

solve log_x (x−3)=log_x (5−x)

$${solve} \\ $$$${log}_{{x}} \left({x}−\mathrm{3}\right)={log}_{{x}} \left(\mathrm{5}−{x}\right) \\ $$

Question Number 88977 Answers: 0 Comments: 1

x^3 + 3^x = 17 x =?

$$\:{x}^{\mathrm{3}} \:+\:\mathrm{3}^{{x}} \:=\:\mathrm{17} \\ $$$${x}\:=? \\ $$

Question Number 88899 Answers: 0 Comments: 14

Simplify ((((35+18i(√3)))^(1/3) +((35−18i(√3)))^(1/3) −4)/3)

$${Simplify} \\ $$$$\frac{\sqrt[{\mathrm{3}}]{\mathrm{35}+\mathrm{18}{i}\sqrt{\mathrm{3}}}+\sqrt[{\mathrm{3}}]{\mathrm{35}−\mathrm{18}{i}\sqrt{\mathrm{3}}}−\mathrm{4}}{\mathrm{3}} \\ $$

Question Number 88892 Answers: 0 Comments: 2

Question Number 88592 Answers: 1 Comments: 0

show that the variance δ^2 of a set of observations x_1 ,x_2 ,...x_n with mean x^_ can be expressed in the form δ^2 = ((Σ_(i=1) ^n x_i ^2 )/n) − x^ ^(2 )

$$\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{variance}\:\delta^{\mathrm{2}} \:\mathrm{of}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{observations}\:{x}_{\mathrm{1}} ,{x}_{\mathrm{2}} ,...{x}_{{n}} \:\mathrm{with}\:\mathrm{mean} \\ $$$$\overset{\_} {{x}}\:\mathrm{can}\:\mathrm{be}\:\mathrm{expressed}\:\mathrm{in}\:\mathrm{the}\:\mathrm{form}\:\:\delta^{\mathrm{2}} \:=\:\frac{\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}{x}_{{i}} ^{\mathrm{2}} }{{n}}\:−\:\bar {{x}}\:^{\mathrm{2}\:} \\ $$

Question Number 88559 Answers: 0 Comments: 1

∫_((−π)/6) ^((3π)/4) ((√(tanx))/(1+(√(tanx))))dx

$$\int_{\frac{−\pi}{\mathrm{6}}} ^{\frac{\mathrm{3}\pi}{\mathrm{4}}} \frac{\sqrt{{tanx}}}{\mathrm{1}+\sqrt{{tanx}}}{dx} \\ $$

Question Number 88494 Answers: 0 Comments: 2

∫ (√(cos(x))) dx

$$\int\:\sqrt{\mathrm{cos}\left(\mathrm{x}\right)}\:\:\mathrm{dx} \\ $$

Question Number 88436 Answers: 0 Comments: 0

show that (for e>1) the equation of a hyperbola with focus (±ae,0) and directrix x = (a/e) is (x^2 /a^2 ) − (y^2 /b^2 ) hence find an equation for the eccencitrity of the hyperbola

$$\:\mathrm{show}\:\mathrm{that}\:\left(\mathrm{for}\:{e}>\mathrm{1}\right)\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{a}\:\mathrm{hyperbola}\:\mathrm{with}\: \\ $$$$\mathrm{focus}\:\:\left(\pm{ae},\mathrm{0}\right)\:\mathrm{and}\:\mathrm{directrix}\:\:{x}\:=\:\frac{{a}}{{e}}\:\mathrm{is}\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }\:−\:\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} } \\ $$$$\:\:\:\mathrm{hence}\:\mathrm{find}\:\mathrm{an}\:\mathrm{equation}\:\mathrm{for}\:\mathrm{the}\:\mathrm{eccencitrity}\:\mathrm{of}\: \\ $$$$\mathrm{the}\:\mathrm{hyperbola} \\ $$

Question Number 88434 Answers: 0 Comments: 2

find the partial derivatives of first and second order for the function f(x,y) = x^3 y + 3xy + y^4

$$\mathrm{find}\:\mathrm{the}\:\mathrm{partial}\:\mathrm{derivatives}\:\mathrm{of}\:\mathrm{first}\:\mathrm{and}\:\mathrm{second}\:\mathrm{order} \\ $$$$\mathrm{for}\:\mathrm{the}\:\mathrm{function} \\ $$$$\:{f}\left({x},{y}\right)\:=\:{x}^{\mathrm{3}} {y}\:+\:\mathrm{3}{xy}\:+\:{y}^{\mathrm{4}} \\ $$

Question Number 88417 Answers: 0 Comments: 1

e^(−z) _1 f_1 (a;b;z)=((Γ(b))/(Γ(b−a))) G_(1,2) ^(1,1) (z∣_(0,1−b) ^(a−b+1) )

$${e}^{−{z}} \:_{\mathrm{1}} {f}_{\mathrm{1}} \left({a};{b};{z}\right)=\frac{\Gamma\left({b}\right)}{\Gamma\left({b}−{a}\right)}\:{G}_{\mathrm{1},\mathrm{2}} ^{\mathrm{1},\mathrm{1}} \left({z}\mid_{\mathrm{0},\mathrm{1}−{b}} ^{{a}−{b}+\mathrm{1}} \right) \\ $$

Question Number 88339 Answers: 3 Comments: 3

∫( (√(tan x )) + (√(cot x)) )dx = ?

$$\:\int\left(\:\sqrt{\mathrm{tan}\:{x}\:}\:+\:\sqrt{\mathrm{cot}\:{x}}\:\right){dx}\:=\:? \\ $$

Question Number 88263 Answers: 1 Comments: 1

prove that ∣((e^z −e^(−z) )/2)∣^2 +cos^2 y=sinh^2 x when z=x+iy