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Question Number 175670 Answers: 1 Comments: 0

Solve the differential equation (1+y^2 )dx−(1+x^2 )xydy=0

$${Solve}\:{the}\:{differential}\:{equation} \\ $$$$\left(\mathrm{1}+{y}^{\mathrm{2}} \right){dx}−\left(\mathrm{1}+{x}^{\mathrm{2}} \right){xydy}=\mathrm{0} \\ $$

Question Number 181509 Answers: 1 Comments: 0

Solve: (dy/dx)=((y^2 −3xy−5x^2 )/x^2 ) y(1)=−1 M.m

$$\mathrm{Solve}: \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{y}^{\mathrm{2}} −\mathrm{3xy}−\mathrm{5x}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{1}\right)=−\mathrm{1} \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 175655 Answers: 1 Comments: 0

Question Number 175653 Answers: 2 Comments: 0

Q: prove that the following equation has no solution. (√(x +⌊ x ⌋)) + (√(x −(√x) )) = 1

$$ \\ $$$$\:\:\:{Q}:\:\:{prove}\:{that}\:{the}\:{following} \\ $$$$\:\:\:\:\:{equation}\:{has}\:{no}\:{solution}. \\ $$$$ \\ $$$$\:\:\:\sqrt{{x}\:+\lfloor\:{x}\:\rfloor}\:+\:\sqrt{{x}\:−\sqrt{{x}}\:}\:=\:\mathrm{1} \\ $$$$ \\ $$

Question Number 175650 Answers: 0 Comments: 0

cos(5x)= a.cos^( 5) (x)+b.cos^( 4) (x)+c.cos^3 (x)+ d.cos^( 2) (x)+e.cos(x)+f a , b , c , d , e , f =?

$$\: \\ $$$$ \\ $$$${cos}\left(\mathrm{5}{x}\right)=\:{a}.{cos}^{\:\mathrm{5}} \left({x}\right)+{b}.{cos}^{\:\mathrm{4}} \left({x}\right)+{c}.{cos}^{\mathrm{3}} \left({x}\right)+\:{d}.{cos}^{\:\mathrm{2}} \left({x}\right)+{e}.{cos}\left({x}\right)+{f} \\ $$$$\:\:\:\:\:\:{a}\:,\:{b}\:,\:{c}\:,\:{d}\:,\:{e}\:,\:{f}\:=? \\ $$$$ \\ $$$$ \\ $$

Question Number 175652 Answers: 0 Comments: 0

Question Number 175644 Answers: 0 Comments: 0

Question Number 175639 Answers: 1 Comments: 0

x^(99) +y^(99) = x^(100) Interger solutions?

$${x}^{\mathrm{99}} +{y}^{\mathrm{99}} =\:{x}^{\mathrm{100}} \\ $$$${Interger}\:{solutions}?\: \\ $$

Question Number 175638 Answers: 0 Comments: 0

Ω = ∫_0 ^( (π/2)) (( sin( 3x ))/( (√( 1− sin(x).cos(x))))) dx = 2((√( a)) .ln( 1 + (√(b )) ) + c ) find the value of : a + b + c = ? ■ m.n

$$\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\:\:{sin}\left(\:\mathrm{3}{x}\:\right)}{\:\sqrt{\:\mathrm{1}−\:{sin}\left({x}\right).{cos}\left({x}\right)}}\:{dx}\:=\:\mathrm{2}\left(\sqrt{\:{a}}\:.{ln}\left(\:\mathrm{1}\:+\:\sqrt{{b}\:}\:\:\right)\:+\:{c}\:\right) \\ $$$$ \\ $$$${find}\:{the}\:{value}\:{of}\::\:\:\:\:\:\:{a}\:+\:{b}\:+\:{c}\:=\:?\:\:\:\:\:\:\:\:\:\:\blacksquare\:{m}.{n} \\ $$$$\: \\ $$

Question Number 175637 Answers: 1 Comments: 0

Question Number 175620 Answers: 0 Comments: 1

the domain of f(x) = (√(log_x {x})) ; {.} denote the fractional part is

$${the}\:{domain}\:{of}\:\:{f}\left({x}\right)\:\:=\:\:\sqrt{\mathrm{log}_{{x}} \left\{{x}\right\}}\:\:; \\ $$$$\left\{.\right\}\:{denote}\:{the}\:{fractional}\:{part}\:{is} \\ $$

Question Number 175618 Answers: 1 Comments: 2

Question Number 175614 Answers: 1 Comments: 0

∫(1/(4t^3 +3t^2 +4t+1))dt

$$\int\frac{\mathrm{1}}{\mathrm{4}{t}^{\mathrm{3}} +\mathrm{3}{t}^{\mathrm{2}} +\mathrm{4}{t}+\mathrm{1}}{dt} \\ $$

Question Number 175608 Answers: 1 Comments: 3

Question Number 175602 Answers: 1 Comments: 2

∫ (dx/(csc x+ cos x)) =?

$$\:\int\:\frac{\mathrm{dx}}{\mathrm{csc}\:\mathrm{x}+\:\mathrm{cos}\:\mathrm{x}}\:=? \\ $$

Question Number 175601 Answers: 2 Comments: 0

Question Number 175623 Answers: 1 Comments: 0

min f(x)=(√(x^2 −2x+5)) +(√(4x^2 −4x+10))

$$\:\mathrm{min}\:\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{5}}\:+\sqrt{\mathrm{4x}^{\mathrm{2}} −\mathrm{4x}+\mathrm{10}} \\ $$

Question Number 175624 Answers: 3 Comments: 0

let p(x) = x^6 +ax^5 +bx^4 +cx^3 +dx^2 +ex+f be a polynomial function such that p(1) = 1 ; p(2) = 2 ; p(3) = 3 p(4) = 4 ; p(5) = 5 ; p(6) = 6 then find p(7) = ?

Question Number 175595 Answers: 0 Comments: 0

Question Number 175593 Answers: 0 Comments: 3

If 0<a≤b then prove that: determinant ((1,a,(log(a^a ))),(1,((√((a^2 +b^2 )/2)) (√((a^2 +b^2 )/8)) ∙ log(((a^2 +b^2 )/2))),),(1,b,(log(b^b ))))≥ 0

$$\mathrm{If}\:\:\:\mathrm{0}<\mathrm{a}\leqslant\mathrm{b}\:\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\begin{vmatrix}{\mathrm{1}}&{\mathrm{a}}&{\mathrm{log}\left(\mathrm{a}^{\boldsymbol{\mathrm{a}}} \right)}\\{\mathrm{1}}&{\sqrt{\frac{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} }{\mathrm{2}}}\:\sqrt{\frac{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} }{\mathrm{8}}}\:\centerdot\:\mathrm{log}\left(\frac{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} }{\mathrm{2}}\right)}&{}\\{\mathrm{1}}&{\mathrm{b}}&{\mathrm{log}\left(\mathrm{b}^{\boldsymbol{\mathrm{b}}} \right)}\end{vmatrix}\geqslant\:\mathrm{0} \\ $$

Question Number 175588 Answers: 2 Comments: 1

Question Number 175585 Answers: 1 Comments: 6

in AB^Δ C prove that: sin ((( A)/2) ) ≤ (( a)/( b + c)) ■

$$ \\ $$$$\:\:\:{in}\:{A}\overset{\Delta} {{B}C}\:\:{prove}\:\:{that}: \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:{sin}\:\left(\frac{\:{A}}{\mathrm{2}}\:\right)\:\leqslant\:\frac{\:{a}}{\:{b}\:+\:{c}}\:\:\:\:\:\:\:\blacksquare \\ $$$$ \\ $$

Question Number 175583 Answers: 0 Comments: 1

∫_0 ^2 x^t dt=3 solve for x

$$\int_{\mathrm{0}} ^{\mathrm{2}} {x}^{{t}} {dt}=\mathrm{3} \\ $$$${solve}\:{for}\:{x} \\ $$

Question Number 175579 Answers: 0 Comments: 0

lim_(x→∞) ((x^(1−sin ((1/x))) .(x^(sin ((1/x))) −1))/(ln x))

$$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{1}−\mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)} .\left(\mathrm{x}^{\mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)} −\mathrm{1}\right)}{\mathrm{ln}\:\mathrm{x}} \\ $$

Question Number 175573 Answers: 0 Comments: 0

Question Number 175572 Answers: 0 Comments: 0

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