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Question Number 36180 Answers: 1 Comments: 1

calculate ∫_0 ^1 ((ln(t))/((1+t)^2 ))dt

$${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left({t}\right)}{\left(\mathrm{1}+{t}\right)^{\mathrm{2}} }{dt} \\ $$

Question Number 36179 Answers: 0 Comments: 1

let f(x,y) = ((xy)/(x+y)) 1) find D_f 2)calcule x(∂f/∂x)(x,y) +y (∂f/∂y)(x,y) interms of f(x,y)

$${let}\:{f}\left({x},{y}\right)\:=\:\frac{{xy}}{{x}+{y}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right){calcule}\:{x}\frac{\partial{f}}{\partial{x}}\left({x},{y}\right)\:+{y}\:\frac{\partial{f}}{\partial{y}}\left({x},{y}\right)\:{interms}\:{of}\:{f}\left({x},{y}\right) \\ $$

Question Number 36178 Answers: 0 Comments: 1

let f(x,y)=ln((√(x^2 +y^2 ))) calculate (∂^2 f/∂x^2 )(x,y)+(∂^2 f/∂y^2 )

$${let}\:{f}\left({x},{y}\right)={ln}\left(\sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }\right)\: \\ $$$${calculate}\:\frac{\partial^{\mathrm{2}} {f}}{\partial{x}^{\mathrm{2}} }\left({x},{y}\right)+\frac{\partial^{\mathrm{2}} {f}}{\partial{y}^{\mathrm{2}} } \\ $$

Question Number 36177 Answers: 0 Comments: 1

let f(x)= arctan((x/y)) calculate (∂^2 f/∂x^2 )(x,y) , (∂^2 f/∂y^2 )(x,y), (∂^2 f/(∂x∂y))(x,y) (∂^2 f/(∂y∂x))(x,y)

$${let}\:{f}\left({x}\right)=\:{arctan}\left(\frac{{x}}{{y}}\right) \\ $$$${calculate}\:\:\frac{\partial^{\mathrm{2}} {f}}{\partial{x}^{\mathrm{2}} }\left({x},{y}\right)\:,\:\frac{\partial^{\mathrm{2}} {f}}{\partial{y}^{\mathrm{2}} }\left({x},{y}\right),\:\frac{\partial^{\mathrm{2}} {f}}{\partial{x}\partial{y}}\left({x},{y}\right) \\ $$$$\frac{\partial^{\mathrm{2}} {f}}{\partial{y}\partial{x}}\left({x},{y}\right) \\ $$

Question Number 36176 Answers: 0 Comments: 0

let f(x,y) =(x^2 +y^2 )sin{ (1/(√(x^2 +y^2 )))} if(x,y)=(0,0) and f(0,0)=0 prove that f is differenciable at all point of R^2 2) prove that (∂f/∂x) and (∂f/∂y) are not differdnciable at (0,0)

$${let}\:{f}\left({x},{y}\right)\:=\left({x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right){sin}\left\{\:\frac{\mathrm{1}}{\sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }}\right\}\:{if}\left({x},{y}\right)=\left(\mathrm{0},\mathrm{0}\right) \\ $$$${and}\:{f}\left(\mathrm{0},\mathrm{0}\right)=\mathrm{0} \\ $$$${prove}\:{that}\:{f}\:{is}\:{differenciable}\:{at}\:{all}\:{point}\:{of}\:{R}^{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\frac{\partial{f}}{\partial{x}}\:{and}\:\frac{\partial{f}}{\partial{y}}\:{are}\:{not}\:{differdnciable} \\ $$$${at}\:\left(\mathrm{0},\mathrm{0}\right) \\ $$

Question Number 36175 Answers: 0 Comments: 0

let g(x,y) = ((1+x+y)/(x^2 −y^2 )) is g have a limit at (0,0)?

$${let}\:{g}\left({x},{y}\right)\:=\:\frac{\mathrm{1}+{x}+{y}}{{x}^{\mathrm{2}} \:−{y}^{\mathrm{2}} } \\ $$$${is}\:{g}\:{have}\:{a}\:{limit}\:{at}\:\left(\mathrm{0},\mathrm{0}\right)? \\ $$

Question Number 36174 Answers: 0 Comments: 0

find lim_((x,y)→(0,0)) ((1−cos((√(xy))))/y)

$${find}\:{lim}_{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)} \:\:\:\frac{\mathrm{1}−{cos}\left(\sqrt{{xy}}\right)}{{y}} \\ $$

Question Number 36173 Answers: 0 Comments: 1

calculate (∂f/∂x) and (∂f/∂y) in this cases 1) f(x,y)= e^(−x) sin(2y +1) 2)f(x,y) =(x^2 +y^2 )e^(−xy) 3)f(x,y) = (x/(x^2 +y^2 ))

$${calculate}\:\frac{\partial{f}}{\partial{x}}\:{and}\:\frac{\partial{f}}{\partial{y}}\:{in}\:{this}\:{cases} \\ $$$$\left.\mathrm{1}\right)\:{f}\left({x},{y}\right)=\:{e}^{−{x}} \:{sin}\left(\mathrm{2}{y}\:+\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right){f}\left({x},{y}\right)\:=\left({x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right){e}^{−{xy}} \\ $$$$\left.\mathrm{3}\right){f}\left({x},{y}\right)\:=\:\frac{{x}}{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} } \\ $$

Question Number 36168 Answers: 0 Comments: 3

let A(t) = ∫_(−∞) ^(+∞) ((sin(xt))/(( x +1+i)^2 )) dx with t from R 2) calculate A(t) 2) extract Re(A(t)) and Im(A(t)) 3) find the value of ∫_(−∞) ^(+∞) ((cos(3x))/((x+1+i)^2 ))dx

$${let}\:{A}\left({t}\right)\:=\:\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{sin}\left({xt}\right)}{\left(\:{x}\:+\mathrm{1}+{i}\right)^{\mathrm{2}} }\:{dx}\:\:{with}\:{t}\:{from}\:{R} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{A}\left({t}\right) \\ $$$$\left.\mathrm{2}\right)\:{extract}\:{Re}\left({A}\left({t}\right)\right)\:{and}\:{Im}\left({A}\left({t}\right)\right) \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\frac{{cos}\left(\mathrm{3}{x}\right)}{\left({x}+\mathrm{1}+{i}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 36167 Answers: 0 Comments: 2

let give I = ∫_0 ^∞ (dx/((x^2 +i)^2 )) 1) extract Re(I) and Im(I) 2) find the value of I 3) calculate Re(I) and Im(I) .

$${let}\:{give}\:\:{I}\:\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+{i}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right)\:{extract}\:{Re}\left({I}\right)\:{and}\:{Im}\left({I}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:{I} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{Re}\left({I}\right)\:{and}\:{Im}\left({I}\right)\:. \\ $$

Question Number 36166 Answers: 0 Comments: 1

Find the middle term in the expansion of (x^ + (3/x))^9

$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{middle}\:\mathrm{term}\:\mathrm{in}\: \\ $$$$\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\:\left(\mathrm{x}^{} \:+\:\frac{\mathrm{3}}{\mathrm{x}}\right)^{\mathrm{9}} \\ $$

Question Number 36163 Answers: 0 Comments: 3

Question Number 36154 Answers: 0 Comments: 0

Q. If x≠y≠z and determinant ((x,x^3 ,(x^4 −1)),(y,y^3 ,(y^4 −1)),((z ),z^3 ,(z^4 −1)))=0 Prove that xyz(xy+yz+zx)=(x+y+z) please help.

$${Q}.\:\:{If}\:{x}\neq{y}\neq{z}\:\:{and}\:\:\begin{vmatrix}{{x}}&{{x}^{\mathrm{3}} }&{{x}^{\mathrm{4}} −\mathrm{1}}\\{{y}}&{{y}^{\mathrm{3}} }&{{y}^{\mathrm{4}} −\mathrm{1}}\\{{z}\:}&{{z}^{\mathrm{3}} }&{{z}^{\mathrm{4}} −\mathrm{1}}\end{vmatrix}=\mathrm{0} \\ $$$$ \\ $$$${Prove}\:{that}\:\:{xyz}\left({xy}+{yz}+{zx}\right)=\left({x}+{y}+{z}\right) \\ $$$$ \\ $$$${please}\:{help}. \\ $$

Question Number 36153 Answers: 0 Comments: 1

(((x+yi−2)^2 )/(x−yi+1))

$$\frac{\left({x}+{yi}−\mathrm{2}\right)^{\mathrm{2}} }{{x}−{yi}+\mathrm{1}} \\ $$

Question Number 36140 Answers: 1 Comments: 1

Question Number 36148 Answers: 0 Comments: 0

[2^x −^(+ 3) 1 4^(2y+x) x6]=[3^(0−7) 2x]

$$ \\ $$$$\:\:\left[\overset{\mathrm{x}} {\mathrm{2}}\overset{+\:\:\mathrm{3}} {−}\mathrm{1}\:\:\:\:\overset{\mathrm{2y}+\mathrm{x}} {\mathrm{4}x6}\right]=\left[\overset{\mathrm{0}−\mathrm{7}} {\mathrm{3}}\:\mathrm{2x}\right] \\ $$

Question Number 36132 Answers: 0 Comments: 7

a+b=10.........(i) ab+c=0..........(ii) ac+d=6..........(iii) ad=−1...........(iv) (a,b,c,d)=? Note: This problem is related to solve the equation (t^4 +10t+6t−1=0) of Q#35844

$${a}+{b}=\mathrm{10}.........\left(\mathrm{i}\right) \\ $$$${ab}+{c}=\mathrm{0}..........\left(\mathrm{ii}\right) \\ $$$${ac}+{d}=\mathrm{6}..........\left(\mathrm{iii}\right) \\ $$$${ad}=−\mathrm{1}...........\left(\mathrm{iv}\right) \\ $$$$\left({a},{b},{c},{d}\right)=? \\ $$$$\mathcal{N}{ote}:\:{This}\:{problem}\:{is}\:{related}\:{to}\:{solve} \\ $$$${the}\:{equation}\:\left({t}^{\mathrm{4}} +\mathrm{10}{t}+\mathrm{6}{t}−\mathrm{1}=\mathrm{0}\right)\:{of} \\ $$$${Q}#\mathrm{35844} \\ $$

Question Number 36128 Answers: 3 Comments: 3

∫sin^8 xdx ∫sin^6 xdx

$$\int\boldsymbol{\mathrm{sin}}^{\mathrm{8}} \boldsymbol{{xdx}} \\ $$$$\int\boldsymbol{\mathrm{sin}}^{\mathrm{6}} \boldsymbol{{xdx}} \\ $$

Question Number 36126 Answers: 0 Comments: 4

x^4 +10x^3 +6x−1 =^(?) (x^2 +(((√5)−1)/2))(x^2 +10x−(((√5)+1)/2))

$$\mathrm{x}^{\mathrm{4}} +\mathrm{10x}^{\mathrm{3}} +\mathrm{6x}−\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\overset{?} {=}\left({x}^{\mathrm{2}} +\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{2}}\right)\left({x}^{\mathrm{2}} +\mathrm{10}{x}−\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{2}}\right) \\ $$

Question Number 36120 Answers: 1 Comments: 0

3(√(200×1080))

$$\mathrm{3}\sqrt{\mathrm{200}×\mathrm{1080}} \\ $$

Question Number 36119 Answers: 0 Comments: 3

3(√(433^ ))