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Question Number 43226 Answers: 1 Comments: 0

If(x−(1/x)=7)thenthevalueofx^4 +(1/x^4 )is?

$$ \\ $$$${If}\left({x}−\frac{\mathrm{1}}{{x}}=\mathrm{7}\right){thenthevalueofx}^{\mathrm{4}} +\frac{\mathrm{1}}{{x}^{\mathrm{4}} }{is}? \\ $$

Question Number 43224 Answers: 1 Comments: 0

how many square in a chess board.

$${how}\:{many}\:{square}\:{in}\:{a}\:{chess}\:{board}. \\ $$

Question Number 43267 Answers: 0 Comments: 2

cos 2x=2cos^2 −1 cos 3x=4cos^3 x−3cos x cos 4x=8cos^4 x−8cos^2 x+1 cos 5x=16cos^5 x−20cos^3 +5cos x cos 6x=32cos^6 x−48cos^4 x+18cos^2 x−1 cos 7x=64cos^7 x−112cos^5 x+56cos^3 x−4cos x cos 8x=128cos^8 x−256cos^6 x+160cos^4 x−32cos^2 x+1

$$\mathrm{cos}\:\mathrm{2}{x}=\mathrm{2cos}^{\mathrm{2}} −\mathrm{1} \\ $$$$\mathrm{cos}\:\mathrm{3}{x}=\mathrm{4cos}^{\mathrm{3}} \:{x}−\mathrm{3cos}\:{x} \\ $$$$\mathrm{cos}\:\mathrm{4}{x}=\mathrm{8cos}^{\mathrm{4}} \:{x}−\mathrm{8cos}^{\mathrm{2}} \:{x}+\mathrm{1} \\ $$$$\mathrm{cos}\:\mathrm{5}{x}=\mathrm{16cos}^{\mathrm{5}} \:{x}−\mathrm{20cos}^{\mathrm{3}} +\mathrm{5cos}\:{x}\: \\ $$$$\mathrm{cos}\:\mathrm{6}{x}=\mathrm{32cos}^{\mathrm{6}} \:{x}−\mathrm{48cos}^{\mathrm{4}} \:{x}+\mathrm{18cos}^{\mathrm{2}} \:{x}−\mathrm{1} \\ $$$$\mathrm{cos}\:\mathrm{7}{x}=\mathrm{64cos}^{\mathrm{7}} \:{x}−\mathrm{112cos}^{\mathrm{5}} \:{x}+\mathrm{56cos}^{\mathrm{3}} \:{x}−\mathrm{4cos}\:{x} \\ $$$$\mathrm{cos}\:\mathrm{8}{x}=\mathrm{128cos}^{\mathrm{8}} \:{x}−\mathrm{256cos}^{\mathrm{6}} \:{x}+\mathrm{160cos}^{\mathrm{4}} \:{x}−\mathrm{32cos}^{\mathrm{2}} \:{x}+\mathrm{1} \\ $$

Question Number 43266 Answers: 1 Comments: 0

cos^3 x+cos^(−3) x=0 sin 2x+cos 2x=...

$$\mathrm{cos}^{\mathrm{3}} {x}+\mathrm{cos}^{−\mathrm{3}} {x}=\mathrm{0} \\ $$$$\mathrm{sin}\:\mathrm{2}{x}+\mathrm{cos}\:\mathrm{2}{x}=... \\ $$

Question Number 43205 Answers: 1 Comments: 0

Question Number 43196 Answers: 0 Comments: 4

Question Number 43192 Answers: 1 Comments: 6

Question Number 43191 Answers: 1 Comments: 3

integrate by use a partial friction ∫((lnx)/((1+x)^2 ))

$${integrate}\:{by}\:{use}\:{a}\:{partial}\:{friction} \\ $$$$\int\frac{{lnx}}{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} } \\ $$

Question Number 43190 Answers: 1 Comments: 1

a point move in such away that its its distance from the x−axis is alwa yas(1/5) its distance from origin. find the equetion of its path.

$${a}\:{point}\:{move}\:{in}\:{such}\:{away}\:{that}\:{its}\: \\ $$$${its}\:{distance}\:{from}\:{the}\:{x}−{axis}\:{is}\:{alwa} \\ $$$${yas}\frac{\mathrm{1}}{\mathrm{5}}\:{its}\:{distance}\:{from}\:{origin}. \\ $$$${find}\:{the}\:{equetion}\:{of}\:{its}\:{path}. \\ $$

Question Number 43180 Answers: 1 Comments: 1

The smallest and the largest values of tan^(−1) (((1−x)/(1+x))) , 0≤ x ≤ 1 are

$$\mathrm{The}\:\mathrm{smallest}\:\mathrm{and}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{values}\:\mathrm{of} \\ $$$$\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right)\:,\:\:\mathrm{0}\leqslant\:{x}\:\leqslant\:\mathrm{1}\:\:\mathrm{are} \\ $$

Question Number 43179 Answers: 1 Comments: 0

The solution of sin^(−1) (((2a)/(1+a^2 )))−cos^(−1) (((1−b^2 )/(1+b^2 )))=tan^(−1) (((2x)/(1−x^2 ))) is

$$\mathrm{The}\:\mathrm{solution}\:\mathrm{of} \\ $$$$\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{2}{a}}{\mathrm{1}+{a}^{\mathrm{2}} }\right)−\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{1}−{b}^{\mathrm{2}} }{\mathrm{1}+{b}^{\mathrm{2}} }\right)=\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{2}{x}}{\mathrm{1}−{x}^{\mathrm{2}} }\right)\:\mathrm{is} \\ $$

Question Number 43187 Answers: 2 Comments: 1

Question Number 43159 Answers: 1 Comments: 0

Question Number 43158 Answers: 2 Comments: 1

∫cosecxdx

$$\int{cosecxdx} \\ $$

Question Number 43157 Answers: 1 Comments: 2

∫secxdx

$$\int{secxdx} \\ $$

Question Number 43156 Answers: 1 Comments: 0

integrate w.r.t x ∫((xe^x )/(√(1+x^2 )))dx

$${integrate}\:{w}.{r}.{t}\:{x} \\ $$$$\int\frac{{xe}^{{x}} }{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 43170 Answers: 1 Comments: 3

let A_n = ∫_0 ^∞ [n e^(−x) ]dx with n integr natural. 1) calculate A_n 2) find lim_(n→+∞) A_n .

$${let}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\left[{n}\:{e}^{−{x}} \right]{dx}\:\:{with}\:{n}\:{integr}\:{natural}. \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} . \\ $$

Question Number 43147 Answers: 0 Comments: 2

If ∫_0 ^∞ e^(−x^2 ) dx = ((√π)/(2 )) , then prove that ∫_0 ^∞ e^(−ax^2 ) dx = (√(π/(4a))) where a>0.

$$\mathrm{If}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−{x}^{\mathrm{2}} } {dx}\:=\:\frac{\sqrt{\pi}}{\mathrm{2}\:}\:, \\ $$$$\mathrm{then}\:{prove}\:{that}\:\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\mathrm{a}{x}^{\mathrm{2}} } {dx}\:=\:\sqrt{\frac{\pi}{\mathrm{4a}}} \\ $$$$\mathrm{where}\:\mathrm{a}>\mathrm{0}. \\ $$

Question Number 43145 Answers: 1 Comments: 4

∫_0 ^∞ [ 2e^(−x) ]dx = ? where [.]= gif.

$$\int_{\mathrm{0}} ^{\infty} \:\left[\:\mathrm{2e}^{−{x}} \right]{dx}\:=\:?\: \\ $$$${where}\:\left[.\right]=\:{gif}. \\ $$

Question Number 43135 Answers: 1 Comments: 4

Construct a triangle ΔABC with ∠B=50° AC=6 cm AB+BC=8 cm see also Q42942.

$${Construct}\:{a}\:{triangle}\:\Delta{ABC}\:{with} \\ $$$$\angle{B}=\mathrm{50}° \\ $$$${AC}=\mathrm{6}\:{cm} \\ $$$${AB}+{BC}=\mathrm{8}\:{cm} \\ $$$$ \\ $$$${see}\:{also}\:{Q}\mathrm{42942}. \\ $$

Question Number 43131 Answers: 2 Comments: 1

Question Number 43125 Answers: 1 Comments: 1

Question Number 43100 Answers: 1 Comments: 2

let f(x) = ∫_0 ^(π/2) ((cosθ)/(1+xsinθ))dθ 1) determine a explicit form of f(x) 2) calculate ∫_0 ^(π/2) ((sin(2θ))/((1+xsinθ)^2 ))dθ 3) find the values of ∫_0 ^(π/2) ((cosθ)/(1+2cosθ))dθ and ∫_0 ^(π/2) ((sin(2θ))/((1+3sinθ)^2 ))dθ .

$${let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\frac{{cos}\theta}{\mathrm{1}+{xsin}\theta}{d}\theta \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{sin}\left(\mathrm{2}\theta\right)}{\left(\mathrm{1}+{xsin}\theta\right)^{\mathrm{2}} }{d}\theta \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{values}\:{of}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{cos}\theta}{\mathrm{1}+\mathrm{2}{cos}\theta}{d}\theta\:\:\:{and}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\frac{{sin}\left(\mathrm{2}\theta\right)}{\left(\mathrm{1}+\mathrm{3}{sin}\theta\right)^{\mathrm{2}} }{d}\theta\:. \\ $$

Question Number 43080 Answers: 0 Comments: 4

Question Number 43072 Answers: 1 Comments: 0

Question Number 43064 Answers: 0 Comments: 8

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