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AllQuestion and Answers: Page 125

Question Number 210679 Answers: 2 Comments: 0

Question Number 210608 Answers: 2 Comments: 1

Question Number 210607 Answers: 3 Comments: 0

Question Number 210606 Answers: 2 Comments: 0

Question Number 210605 Answers: 2 Comments: 0

Question Number 210601 Answers: 1 Comments: 0

Find the value of : Ω = ∫_0 ^( 1) ∫_0 ^( (√(1−x^2 ))) ∫_(√( x^( 2) +y^( 2) )) ^( (√(2−x^2 −y^2 ))) xy dz dy dx =?

$$ \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:{Find}\:\:{the}\:\:{value}\:{of}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \:\int_{\sqrt{\:{x}^{\:\mathrm{2}} \:+{y}^{\:\mathrm{2}} }} ^{\:\sqrt{\mathrm{2}−{x}^{\mathrm{2}} \:−{y}^{\mathrm{2}} }} \:{xy}\:{dz}\:{dy}\:{dx}\:=?\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\: \\ $$

Question Number 210593 Answers: 1 Comments: 0

∫ ((sin x cos x)/( ((cos 2x))^(1/3) + (√(cos 2x)))) dx =? ∫ (dx/(sec x ((sin x))^(1/2) + cos x ((cosec^5 x))^(1/3) )) =?

$$\:\:\int\:\frac{\mathrm{sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x}}{\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{2x}}\:+\:\sqrt{\mathrm{cos}\:\mathrm{2x}}}\:\mathrm{dx}\:=? \\ $$$$\:\:\int\:\frac{\mathrm{dx}}{\mathrm{sec}\:\mathrm{x}\:\sqrt[{\mathrm{2}}]{\mathrm{sin}\:\mathrm{x}}\:+\:\mathrm{cos}\:\mathrm{x}\:\sqrt[{\mathrm{3}}]{\mathrm{cosec}\:^{\mathrm{5}} \mathrm{x}}}\:=? \\ $$

Question Number 210591 Answers: 3 Comments: 0

If a + b = 1 a^2 + b^2 = 2 then, a^(11) + b^(11) = ??

$$\mathrm{If} \\ $$$$\:\:\:\:\mathrm{a}\:\:+\:\:\mathrm{b}\:\:=\:\:\mathrm{1} \\ $$$$\:\:\:\mathrm{a}^{\mathrm{2}} \:\:+\:\:\mathrm{b}^{\mathrm{2}} \:\:=\:\:\mathrm{2} \\ $$$$\mathrm{then},\:\:\:\:\:\mathrm{a}^{\mathrm{11}} \:\:+\:\:\mathrm{b}^{\mathrm{11}} \:\:=\:\:?? \\ $$

Question Number 210590 Answers: 0 Comments: 0

Question Number 210587 Answers: 0 Comments: 3

f(x)= (√( 13 −12(√x) )) + (√(25 −24(√(1−x)) )) find : Min ( f )=?

$$ \\ $$$$\:\:\:\:\:{f}\left({x}\right)=\:\sqrt{\:\mathrm{13}\:−\mathrm{12}\sqrt{{x}}\:\:}\:+\:\sqrt{\mathrm{25}\:−\mathrm{24}\sqrt{\mathrm{1}−{x}}\:} \\ $$$$ \\ $$$$\:\:\:\:\:\:{find}\::\:\:\:\:\mathrm{M}{in}\:\left(\:{f}\:\right)=? \\ $$$$ \\ $$$$ \\ $$

Question Number 210581 Answers: 1 Comments: 0

{ ((x^2 +3x−(√(x^2 +3x−1 = 7)))),((2(√2) sin y = x)) :} x=? and y=?

$$\:\:\begin{cases}{{x}^{\mathrm{2}} +\mathrm{3}{x}−\sqrt{{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{1}\:=\:\mathrm{7}}}\\{\mathrm{2}\sqrt{\mathrm{2}}\:\mathrm{sin}\:{y}\:=\:{x}}\end{cases} \\ $$$$\:\:\:{x}=?\:\:\:\:{and}\:\:\:\:{y}=? \\ $$

Question Number 210579 Answers: 0 Comments: 4

Please... Can anyone help me.. Find the value(s) of x, if (x−2)^((x^2 −2x+4)) =3

$${Please}...\:{Can}\:{anyone}\:{help}\:{me}.. \\ $$$$ \\ $$$$\:{Find}\:{the}\:{value}\left({s}\right)\:{of}\:{x},\:{if} \\ $$$$\:\:\:\left({x}−\mathrm{2}\right)^{\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{4}\right)} =\mathrm{3} \\ $$$$ \\ $$

Question Number 210574 Answers: 3 Comments: 0

if the roots of the equation x^2 +(k+1)x+k=0 are α and β, find the value of the real constant k for which α=2β

$${if}\:{the}\:{roots}\:{of}\:{the}\:{equation}\: \\ $$$${x}^{\mathrm{2}} +\left({k}+\mathrm{1}\right){x}+{k}=\mathrm{0} \\ $$$${are}\:\alpha\:{and}\:\beta, \\ $$$$\:{find}\:{the}\:{value}\:{of}\:{the} \\ $$$$\:{real}\:{constant}\:{k}\:{for} \\ $$$${which}\:\alpha=\mathrm{2}\beta \\ $$

Question Number 210573 Answers: 1 Comments: 0

Question Number 210572 Answers: 1 Comments: 0

Question Number 210571 Answers: 1 Comments: 0

If x,y,z∈R^+ and x^2 +y^2 +z^2 =3 Prove that (1/(4−x)) + (1/(4−y)) + (1/(4−z)) ≤ 1

$$\mathrm{If}\:\:\mathrm{x},\mathrm{y},\mathrm{z}\in\mathrm{R}^{+} \:\:\mathrm{and}\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{3} \\ $$$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{4}−\mathrm{x}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{4}−\mathrm{y}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{4}−\mathrm{z}}\:\:\leqslant\:\:\mathrm{1} \\ $$

Question Number 210566 Answers: 1 Comments: 0

Prove that: if (x∈]−(π/2),(π/2)[ y =∫^( x) _( 0) (dt/(cos(t))) ) ⇒ (y∈IR x =∫^( y) _( 0) (dt/(cosh(t))) )

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{if}\:\left(\mathrm{x}\in\right]−\frac{\pi}{\mathrm{2}},\frac{\pi}{\mathrm{2}}\left[\:\:\mathrm{y}\:=\underset{\:\mathrm{0}} {\int}^{\:\mathrm{x}} \frac{\mathrm{dt}}{\mathrm{cos}\left(\mathrm{t}\right)}\:\right)\:\Rightarrow\:\:\left(\mathrm{y}\in\mathrm{IR}\:\:\:\mathrm{x}\:=\underset{\:\mathrm{0}} {\int}^{\:\mathrm{y}} \frac{\mathrm{dt}}{\mathrm{cosh}\left(\mathrm{t}\right)}\:\right) \\ $$

Question Number 210565 Answers: 1 Comments: 0

Question Number 210559 Answers: 1 Comments: 0

deg [p(x^2 )∙q(x)]=20 deg[((p(x)^3 )/(q(x)^2 ))]=2 then deg q(x)=?

$${deg}\:\left[{p}\left({x}^{\mathrm{2}} \right)\centerdot{q}\left({x}\right)\right]=\mathrm{20} \\ $$$${deg}\left[\frac{{p}\left({x}\right)^{\mathrm{3}} }{{q}\left({x}\right)^{\mathrm{2}} }\right]=\mathrm{2} \\ $$$${then}\:{deg}\:\:{q}\left({x}\right)=? \\ $$

Question Number 210554 Answers: 1 Comments: 0

Question Number 210549 Answers: 1 Comments: 0

let a sequence be difined as a_n = a_(n−1) + ((2cos ((a_(n−1) /2)))/(2sin ((a_(n−1) /2))−1)) , a_(0 ) = 0 find lim_(n→∞) a_(n ) = ?

$$\mathrm{let}\:\mathrm{a}\:\mathrm{sequence}\:\mathrm{be}\:\mathrm{difined}\:\mathrm{as} \\ $$$$\:\mathrm{a}_{\mathrm{n}} =\:\mathrm{a}_{\mathrm{n}−\mathrm{1}} \:+\:\frac{\mathrm{2cos}\:\left(\frac{\mathrm{a}_{\mathrm{n}−\mathrm{1}} }{\mathrm{2}}\right)}{\mathrm{2sin}\:\left(\frac{\mathrm{a}_{\mathrm{n}−\mathrm{1}} }{\mathrm{2}}\right)−\mathrm{1}}\:\:,\:\mathrm{a}_{\mathrm{0}\:} =\:\mathrm{0} \\ $$$$\mathrm{find}\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{a}_{\mathrm{n}\:} \:=\:? \\ $$

Question Number 210542 Answers: 1 Comments: 2

Question Number 210533 Answers: 1 Comments: 1

Question Number 210524 Answers: 1 Comments: 1

Question Number 210517 Answers: 3 Comments: 2

∫(1/(sinx−cos2x))dx

$$\int\frac{\mathrm{1}}{\mathrm{sin}{x}−\mathrm{cos2}{x}}{dx} \\ $$

Question Number 210516 Answers: 3 Comments: 0

Find: x = ? 1 + 3x + 5x^2 + 7x^3 + 9x^4 + 11x^5 + ... = 15

$$\mathrm{Find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$$$\mathrm{1}\:+\:\mathrm{3x}\:+\:\mathrm{5x}^{\mathrm{2}} \:+\:\mathrm{7x}^{\mathrm{3}} \:+\:\mathrm{9x}^{\mathrm{4}} \:+\:\mathrm{11x}^{\mathrm{5}} \:+\:...\:=\:\mathrm{15} \\ $$

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