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AllQuestion and Answers: Page 172

Question Number 205941 Answers: 1 Comments: 0

2+(2/(2−(2/(2+(2/(2−(2/(2+(2/3))))))))) =?

$$\:\:\:\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{2}}{\mathrm{3}}}}}}\:=?\: \\ $$$$\: \\ $$

Question Number 205938 Answers: 0 Comments: 0

(dx/dt)= y+4z ....(1) (dy/dt) = z−x.....(2) (dz/dt) = x − y....(3) solve the sistem by operator ( elemination method )

$$\frac{{dx}}{{dt}}=\:{y}+\mathrm{4}{z}\:....\left(\mathrm{1}\right) \\ $$$$\frac{{dy}}{{dt}}\:=\:{z}−{x}.....\left(\mathrm{2}\right) \\ $$$$\frac{{dz}}{{dt}}\:=\:{x}\:−\:{y}....\left(\mathrm{3}\right) \\ $$$${solve}\:{the}\:{sistem}\:{by}\:{operator}\:\left(\:{elemination}\:{method}\:\right) \\ $$$$ \\ $$$$ \\ $$

Question Number 205928 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (dx/(1+x^4 +x^8 ))

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{4}} +{x}^{\mathrm{8}} } \\ $$

Question Number 205975 Answers: 0 Comments: 3

As reported some users uploaded wrong pictures. Priviledge of following users are now elevated so that they can delete any post. mr W Rasheed Sindhi ajfour mnjuly1970 cortano12 Frix The above users can now directly delete any post by any user.

$$\mathrm{As}\:\mathrm{reported}\:\mathrm{some}\:\mathrm{users}\:\mathrm{uploaded} \\ $$$$\mathrm{wrong}\:\mathrm{pictures}. \\ $$$$\mathrm{Priviledge}\:\mathrm{of}\:\mathrm{following}\:\mathrm{users}\:\mathrm{are} \\ $$$$\mathrm{now}\:\mathrm{elevated}\:\mathrm{so}\:\mathrm{that}\:\mathrm{they}\:\mathrm{can}\:\mathrm{delete} \\ $$$$\mathrm{any}\:\mathrm{post}. \\ $$$$ \\ $$$$\mathrm{mr}\:\mathrm{W} \\ $$$$\mathrm{Rasheed}\:\mathrm{Sindhi} \\ $$$$\mathrm{ajfour} \\ $$$$\mathrm{mnjuly1970} \\ $$$$\mathrm{cortano12} \\ $$$$\mathrm{Frix} \\ $$$$ \\ $$$$\mathrm{The}\:\mathrm{above}\:\mathrm{users}\:\mathrm{can}\:\mathrm{now}\:\mathrm{directly}\:\mathrm{delete}\:\mathrm{any} \\ $$$$\mathrm{post}\:\mathrm{by}\:\mathrm{any}\:\mathrm{user}. \\ $$

Question Number 205971 Answers: 2 Comments: 1

9 Mathematical Analysis ( I ) (X , d ) is a metric space and { p_n }_(n=1) ^∞ is a sequence in X such that , p_n →^(convergent) p . If , K= {p_n }_(n=1) ^∞ ∪ { p } then prove K , is compact in X .

$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{9}\:\:\mathscr{M}{athematical}\:\:\:\:\mathscr{A}{nalysis}\:\left(\:{I}\:\right) \\ $$$$\:\:\left({X}\:,\:{d}\:\right)\:{is}\:{a}\:{metric}\:{space}\:{and}\:\:\:\:\:\:\: \\ $$$$\:\:\:\left\{\:{p}_{{n}} \right\}_{{n}=\mathrm{1}} ^{\infty} {is}\:{a}\:{sequence}\:{in}\:{X}\: \\ $$$$\:\:\:\:\:{such}\:{that}\:,\:{p}_{{n}} \overset{{convergent}} {\rightarrow}\:{p}\:.\:{If}\:,\:{K}=\:\left\{{p}_{{n}} \right\}_{{n}=\mathrm{1}} ^{\infty} \cup\:\left\{\:{p}\:\right\}\:{then} \\ $$$$\:\:\:\:\:{prove}\:\:{K}\:,\:{is}\:{compact}\:{in}\:{X}\:.\: \\ $$$$\:\:\:\: \\ $$

Question Number 205935 Answers: 1 Comments: 0

∫∫_D (4y^2 sin(xy))dxdy = ??? D: x=y x=0 y=(√(π/2)) 0≤x≤y 0≤y≤(√(π/2))

$$\int\underset{{D}} {\int}\left(\mathrm{4}{y}^{\mathrm{2}} {sin}\left({xy}\right)\right){dxdy}\:\:=\:??? \\ $$$${D}:\:\:\:\:\:\:\:{x}={y}\:\:\:\:\:\:{x}=\mathrm{0}\:\:\:\:\:\:\:{y}=\sqrt{\frac{\pi}{\mathrm{2}}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}\leqslant{x}\leqslant{y}\:\:\:\:\:\:\:\mathrm{0}\leqslant{y}\leqslant\sqrt{\frac{\pi}{\mathrm{2}}} \\ $$

Question Number 205922 Answers: 2 Comments: 0

x = 2 (mod 7) x=3 (mod 4) x=?

$$\:\:\:{x}\:=\:\mathrm{2}\:\left({mod}\:\mathrm{7}\right) \\ $$$$\:\:\:{x}=\mathrm{3}\:\left({mod}\:\mathrm{4}\right) \\ $$$$\:\:\:{x}=? \\ $$

Question Number 205919 Answers: 1 Comments: 0

write the following recursive function in explicit form f(1)=1 f(n+1)=(n+1)f(n)+n!

$$\mathrm{write}\:\mathrm{the}\:\mathrm{following}\:\mathrm{recursive}\:\mathrm{function}\:\mathrm{in}\:\mathrm{explicit}\:\mathrm{form} \\ $$$${f}\left(\mathrm{1}\right)=\mathrm{1} \\ $$$${f}\left({n}+\mathrm{1}\right)=\left({n}+\mathrm{1}\right){f}\left({n}\right)+{n}! \\ $$

Question Number 205916 Answers: 1 Comments: 0

lim_(x→0^+ ) xln(e^x −1)

$${lim}_{{x}\rightarrow\mathrm{0}^{+} } \:\:{xln}\left({e}^{{x}} −\mathrm{1}\right) \\ $$

Question Number 205915 Answers: 1 Comments: 0

Question Number 205914 Answers: 4 Comments: 2

if a+b+c+d+e+f=10 and a^2 +b^2 +c^2 +d^2 +e^2 +f^2 =25, find a_(min) and f_(max) .

$${if}\:{a}+{b}+{c}+{d}+{e}+{f}=\mathrm{10}\:{and} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +{d}^{\mathrm{2}} +{e}^{\mathrm{2}} +{f}^{\mathrm{2}} =\mathrm{25},\:{find} \\ $$$${a}_{{min}} \:{and}\:{f}_{{max}} . \\ $$

Question Number 205910 Answers: 0 Comments: 0

Resuelve la siguiente integral I = ∫(x/(sinh^2 (x)∙ln (sinh (x)) − x∙sinh (x)∙cosh (x))) dx

$${Resuelve}\:{la}\:{siguiente}\:{integral} \\ $$$${I}\:=\:\int\frac{{x}}{\mathrm{sinh}^{\mathrm{2}} \left({x}\right)\centerdot\mathrm{ln}\:\left(\mathrm{sinh}\:\left({x}\right)\right)\:−\:{x}\centerdot\mathrm{sinh}\:\left({x}\right)\centerdot\mathrm{cosh}\:\left({x}\right)}\:{dx} \\ $$

Question Number 205904 Answers: 1 Comments: 0

Question Number 205893 Answers: 0 Comments: 4

Question Number 205892 Answers: 1 Comments: 0

Question Number 205885 Answers: 2 Comments: 0

Find: lim_(n→∞) ()^(1/n) (((2n)),(( n)) ) = ?

$$\mathrm{Find}:\:\:\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\sqrt[{\boldsymbol{\mathrm{n}}}]{}\begin{pmatrix}{\mathrm{2n}}\\{\:\:\mathrm{n}}\end{pmatrix}\:=\:? \\ $$

Question Number 205884 Answers: 2 Comments: 1

Question Number 205880 Answers: 2 Comments: 1

Question Number 205866 Answers: 0 Comments: 0

Question Number 205873 Answers: 1 Comments: 0

∫_0 ^π (1/π^2 ) (x/( (√(1+sin^3 x ))))[(3πcosx+4sinx)sin^2 x+4]dx

$$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{1}}{\pi^{\mathrm{2}} }\:\frac{{x}}{\:\sqrt{\mathrm{1}+\mathrm{sin}^{\mathrm{3}} {x}\:}}\left[\left(\mathrm{3}\pi\mathrm{cos}{x}+\mathrm{4sin}{x}\right)\mathrm{sin}^{\mathrm{2}} {x}+\mathrm{4}\right]{dx}\:\:\: \\ $$

Question Number 205861 Answers: 3 Comments: 0

Question Number 205849 Answers: 0 Comments: 8

if a^a =b^b ; a=b is it true? if it is true then prove it.

$${if}\:{a}^{{a}} ={b}^{{b}} \:\:;\:{a}={b}\:\:{is}\:{it}\:{true}? \\ $$$${if}\:{it}\:{is}\:{true}\:{then}\:{prove}\:{it}. \\ $$

Question Number 205842 Answers: 2 Comments: 0

((32^(32^(32) ) )/9) ≡^R ?

$$\frac{\mathrm{32}^{\mathrm{32}^{\mathrm{32}} } }{\mathrm{9}}\:\overset{\mathrm{R}} {\equiv}\:? \\ $$

Question Number 205833 Answers: 0 Comments: 3

can′t Solve Differantial Equation Diff Equa : (((dy(t))/dt))^2 +4y(t)=8t^2 −32t+28.... Sadly it′s impossible to obtain an exact closed−form expression of the Solution of Diff Equa But if the Runge−Kutta method is used. the value of the function at any one point can be estimated

$$\mathrm{can}'\mathrm{t}\:\mathrm{Solve}\:\mathrm{Differantial}\:\mathrm{Equation} \\ $$$$\mathrm{Diff}\:\mathrm{Equa}\::\:\left(\frac{\mathrm{d}{y}\left({t}\right)}{\mathrm{d}{t}}\right)^{\mathrm{2}} +\mathrm{4}{y}\left({t}\right)=\mathrm{8}{t}^{\mathrm{2}} −\mathrm{32}{t}+\mathrm{28}.... \\ $$$$\mathrm{Sadly}\:\mathrm{it}'\mathrm{s}\:\mathrm{impossible}\:\mathrm{to}\:\mathrm{obtain}\:\mathrm{an}\:\mathrm{exact} \\ $$$$\mathrm{closed}−\mathrm{form}\:\mathrm{expression}\:\mathrm{of}\:\mathrm{the}\:\mathrm{Solution}\:\mathrm{of}\:\mathrm{Diff}\:\mathrm{Equa} \\ $$$$\mathrm{But}\:\mathrm{if}\:\mathrm{the}\:\mathrm{Runge}−\mathrm{Kutta}\:\mathrm{method}\:\mathrm{is}\:\mathrm{used}. \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:\mathrm{at}\:\mathrm{any}\:\mathrm{one}\:\mathrm{point}\:\mathrm{can}\:\mathrm{be}\:\mathrm{estimated} \\ $$

Question Number 205827 Answers: 2 Comments: 0

x^3 +y^3 =1 find the implceat second derivative

$$\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} =\mathrm{1} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{implceat}\:\mathrm{second}\:\mathrm{derivative} \\ $$

Question Number 205825 Answers: 1 Comments: 1

[f′(x)]^2 +4f(x)=8x^2 −32x+28 ⇒f(x)=¿

$$\left[{f}'\left({x}\right)\right]^{\mathrm{2}} +\mathrm{4}{f}\left({x}\right)=\mathrm{8}{x}^{\mathrm{2}} −\mathrm{32}{x}+\mathrm{28} \\ $$$$\Rightarrow{f}\left({x}\right)=¿ \\ $$

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