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Question Number 99529 Answers: 1 Comments: 0

Question Number 99516 Answers: 1 Comments: 0

Question Number 99513 Answers: 0 Comments: 2

x,y,z ∈ R^+ x^2 + y^3 + z^4 = x^4 + y^5 + z^6 Prove that (x^2 /(y^4 +1)) + (y^2 /(z^4 +1)) + (z^2 /(x^4 +1)) ≥ ((x^2 +y^2 +z^2 )/2)

$${x},{y},{z}\:\:\in\:\:\mathbb{R}^{+} \\ $$$${x}^{\mathrm{2}} \:+\:{y}^{\mathrm{3}} \:+\:{z}^{\mathrm{4}} \:\:=\:\:{x}^{\mathrm{4}} \:+\:{y}^{\mathrm{5}} \:+\:{z}^{\mathrm{6}} \\ $$$${Prove}\:\:{that} \\ $$$$\:\:\:\:\:\frac{{x}^{\mathrm{2}} }{{y}^{\mathrm{4}} +\mathrm{1}}\:\:+\:\:\frac{{y}^{\mathrm{2}} }{{z}^{\mathrm{4}} +\mathrm{1}}\:\:+\:\:\frac{{z}^{\mathrm{2}} }{{x}^{\mathrm{4}} +\mathrm{1}}\:\:\geqslant\:\:\frac{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} }{\mathrm{2}} \\ $$

Question Number 99505 Answers: 2 Comments: 2

Question Number 99504 Answers: 4 Comments: 0

Question Number 99503 Answers: 5 Comments: 0

Question Number 99496 Answers: 1 Comments: 0

convergence radius of Σ_(n∈N) 2^n z^(n!)

$${convergence}\:{radius}\:{of}\:\:\underset{{n}\in\mathbb{N}} {\sum}\:\mathrm{2}^{{n}} {z}^{{n}!} \: \\ $$

Question Number 99495 Answers: 2 Comments: 2

solve for x,y ∈ N 7^y +2 = 3^x

$$\mathrm{solve}\:\mathrm{for}\:\mathrm{x},\mathrm{y}\:\in\:\mathbb{N}\: \\ $$$$\mathrm{7}^{\mathrm{y}} +\mathrm{2}\:=\:\mathrm{3}^{\mathrm{x}} \: \\ $$

Question Number 99486 Answers: 0 Comments: 0

∫(√(sinx))

$$\int\sqrt{{sinx}} \\ $$

Question Number 99485 Answers: 2 Comments: 0

∫tan^(1/5) xdx

$$\int{tan}^{\frac{\mathrm{1}}{\mathrm{5}}} {xdx} \\ $$

Question Number 99464 Answers: 2 Comments: 0

solve y^(′′) −2y^′ +y =xe^(−x) sin(2x) withy(o) =−1 and y^′ (0) =0

$$\mathrm{solve}\:\mathrm{y}^{''} \:−\mathrm{2y}^{'} \:+\mathrm{y}\:\:=\mathrm{xe}^{−\mathrm{x}} \:\mathrm{sin}\left(\mathrm{2x}\right)\:\mathrm{withy}\left(\mathrm{o}\right)\:=−\mathrm{1}\:\mathrm{and}\:\mathrm{y}^{'} \left(\mathrm{0}\right)\:=\mathrm{0} \\ $$

Question Number 99463 Answers: 1 Comments: 0

let f(x) =e^(−2x) arctan((3/x^2 )) find f^((n)) (x) and f^((n)) (1) 2) if f(x) =Σ_(n=0) ^∞ a_n (x−1)^n determinate a_n

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{e}^{−\mathrm{2x}} \:\mathrm{arctan}\left(\frac{\mathrm{3}}{\mathrm{x}^{\mathrm{2}} }\right) \\ $$$$\mathrm{find}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{if}\:\mathrm{f}\left(\mathrm{x}\right)\:=\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\mathrm{a}_{\mathrm{n}} \left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{n}} \:\:\:\:\mathrm{determinate}\:\mathrm{a}_{\mathrm{n}} \\ $$

Question Number 99462 Answers: 1 Comments: 0

let f(x) =x^3 +2x−5 1) determine f^(−1) (x) 2) find ∫ ((f^(−1) (x))/(f(x)))dx 3) let u(x) =^3 (√x)+2 find ∫ ((uof^(−1) (x))/(uof(x)))dx

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{x}^{\mathrm{3}} +\mathrm{2x}−\mathrm{5} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{determine}\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\int\:\frac{\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)}{\mathrm{f}\left(\mathrm{x}\right)}\mathrm{dx} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{let}\:\mathrm{u}\left(\mathrm{x}\right)\:=^{\mathrm{3}} \sqrt{\mathrm{x}}+\mathrm{2}\:\:\mathrm{find}\:\int\:\:\frac{\mathrm{uof}^{−\mathrm{1}} \left(\mathrm{x}\right)}{\mathrm{uof}\left(\mathrm{x}\right)}\mathrm{dx} \\ $$

Question Number 99465 Answers: 2 Comments: 0

calculate I =∫ cos^2 x sh(2x)dx and J =∫ sin^2 x ch(2x)dx

$$\mathrm{calculate}\:\mathrm{I}\:=\int\:\mathrm{cos}^{\mathrm{2}} \mathrm{x}\:\mathrm{sh}\left(\mathrm{2x}\right)\mathrm{dx}\:\mathrm{and}\:\mathrm{J}\:=\int\:\mathrm{sin}^{\mathrm{2}} \mathrm{x}\:\mathrm{ch}\left(\mathrm{2x}\right)\mathrm{dx} \\ $$

Question Number 99460 Answers: 1 Comments: 0

determine L(((1−cosx)/x^2 ))

$$\mathrm{determine}\:\mathrm{L}\left(\frac{\mathrm{1}−\mathrm{cosx}}{\mathrm{x}^{\mathrm{2}} }\right) \\ $$

Question Number 99459 Answers: 0 Comments: 0

let h(x)=x sin(2x) even 2π poeriodic developp h at fourier serie

$$\mathrm{let}\:\mathrm{h}\left(\mathrm{x}\right)=\mathrm{x}\:\mathrm{sin}\left(\mathrm{2x}\right)\:\:\mathrm{even}\:\mathrm{2}\pi\:\mathrm{poeriodic}\:\:\mathrm{developp}\:\mathrm{h}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 99458 Answers: 0 Comments: 0

let g(x) =xcosx ,odd and 2π periodic developp g at fourier serie

$$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)\:=\mathrm{xcosx}\:\:,\mathrm{odd}\:\mathrm{and}\:\mathrm{2}\pi\:\mathrm{periodic}\:\mathrm{developp}\:\mathrm{g}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 99456 Answers: 0 Comments: 0

let f(x) =x^3 ,odd and 2π periodic developp f at fourier serie

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{x}^{\mathrm{3}} \:\:,\mathrm{odd}\:\mathrm{and}\:\mathrm{2}\pi\:\mathrm{periodic}\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 99455 Answers: 0 Comments: 0

solve y^(′′) −sin(2x)y^′ =((sinx)/x)

$$\mathrm{solve}\:\mathrm{y}^{''} \:−\mathrm{sin}\left(\mathrm{2x}\right)\mathrm{y}^{'} \:\:\:=\frac{\mathrm{sinx}}{\mathrm{x}} \\ $$

Question Number 99494 Answers: 0 Comments: 0

W=f(x,y,z),g(x,y)=C_1 , h(y,z)=C_2 find (dw/dx) ,(dw/dy) ? help me sir pleas i want this

$${W}={f}\left({x},{y},{z}\right),{g}\left({x},{y}\right)={C}_{\mathrm{1}} \:,\:{h}\left({y},{z}\right)={C}_{\mathrm{2}} \:\:{find}\:\frac{{dw}}{{dx}}\:,\frac{{dw}}{{dy}}\:\:?\: \\ $$$$ \\ $$$${help}\:{me}\:{sir}\:{pleas}\:{i}\:{want}\:{this}\: \\ $$

Question Number 99433 Answers: 2 Comments: 1

sin7φ+cos2φ=−2 Find,φ

$${sin}\mathrm{7}\phi+{cos}\mathrm{2}\phi=−\mathrm{2} \\ $$$${Find},\phi \\ $$

Question Number 99430 Answers: 1 Comments: 0

Question Number 99429 Answers: 0 Comments: 0

Solve for n in the equation A_n ^(n−2) =56 {where A_n ^r =n−permution r}

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{n}\:\mathrm{in}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{A}_{\mathrm{n}} ^{\mathrm{n}−\mathrm{2}} =\mathrm{56}\:\left\{\mathrm{where}\:\mathrm{A}_{\mathrm{n}} ^{\mathrm{r}} =\mathrm{n}−\mathrm{permution}\:\mathrm{r}\right\} \\ $$

Question Number 99421 Answers: 0 Comments: 0

Question Number 99413 Answers: 1 Comments: 0

∫_0 ^(+∞) ((sin(ax))/(e^(2πx) −1))dx

$$\int_{\mathrm{0}} ^{+\infty} \frac{{sin}\left({ax}\right)}{{e}^{\mathrm{2}\pi{x}} −\mathrm{1}}{dx} \\ $$

Question Number 99411 Answers: 0 Comments: 2

Solve the equation xa^(1/x) +(1/x)a^x =2a where,a{−1,0,1}

$${Solve}\:{the}\:{equation} \\ $$$${xa}^{\frac{\mathrm{1}}{{x}}} +\frac{\mathrm{1}}{{x}}{a}^{{x}} =\mathrm{2}{a} \\ $$$${where},{a}\left\{−\mathrm{1},\mathrm{0},\mathrm{1}\right\} \\ $$

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