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AllQuestion and Answers: Page 75

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)=¿

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

Question Number 205826 Answers: 0 Comments: 0

f_([0;3]) (x)>0 f(0)=3 f(3)=8 ∫^3 _0 (([f′(x)]^2 )/(f(x)+1))dx = (4/3) f(2)=¿

$$\underset{\left[\mathrm{0};\mathrm{3}\right]} {{f}}\left({x}\right)>\mathrm{0} \\ $$$${f}\left(\mathrm{0}\right)=\mathrm{3} \\ $$$${f}\left(\mathrm{3}\right)=\mathrm{8} \\ $$$$\underset{\mathrm{0}} {\int}^{\mathrm{3}} \frac{\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{{f}\left({x}\right)+\mathrm{1}}{dx}\:=\:\frac{\mathrm{4}}{\mathrm{3}} \\ $$$${f}\left(\mathrm{2}\right)=¿ \\ $$

Question Number 205817 Answers: 2 Comments: 0

2^( x + log_2 3) = 12 ⇒ find: x = ?