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Question Number 115300 Answers: 1 Comments: 0

find from fourier series an expression for log(tanx)

$${find}\:{from}\:{fourier}\:{series}\:{an} \\ $$$${expression}\:{for} \\ $$$$\mathrm{log}\left(\mathrm{tan}{x}\right) \\ $$

Question Number 115298 Answers: 1 Comments: 2

(d^2 y/dx^2 )+log(y)=0

$$\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }+\mathrm{log}\left(\mathrm{y}\right)=\mathrm{0} \\ $$

Question Number 115294 Answers: 2 Comments: 0

Given that N=1×2×3×...×500 is the product of the positive integers from 1 to 500. If N is divisible by 6^k , find the largest possible value of k.

$$\mathrm{Given}\:\mathrm{that}\:{N}=\mathrm{1}×\mathrm{2}×\mathrm{3}×...×\mathrm{500}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{product}\:\mathrm{of}\:\mathrm{the}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{from}\:\mathrm{1}\:\mathrm{to}\:\mathrm{500}. \\ $$$$ \\ $$$$\mathrm{If}\:{N}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{6}^{{k}} ,\:\mathrm{find}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{possible} \\ $$$$\mathrm{value}\:\mathrm{of}\:{k}. \\ $$

Question Number 115285 Answers: 0 Comments: 0

...♠nice topology ♠... suppose ⟨S , τ ⟩ is Baire′s space and S = ∪_(n=1) ^∞ F_n such that F_n ′s are closed sets prove that:: ∃ m ; F_m ^( °) ≠ ∅ ..m.n.july ...♣m.n.july.1970♣...

$$\:\:\:\:\:\:\:\:...\spadesuit{nice}\:\:\:{topology}\:\spadesuit... \\ $$$${suppose}\:\:\langle{S}\:,\:\tau\:\rangle\:{is}\:\:{Baire}'{s} \\ $$$${space}\:\:\:{and}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{S}\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\cup}}{F}_{{n}} \:\:\:{such} \\ $$$${that}\:\:{F}_{{n}} '{s}\:\:{are}\:{closed}\:{sets}\: \\ $$$$\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\exists\:{m}\:;\:{F}_{{m}} ^{\:°} \:\neq\:\varnothing\:\:\:..{m}.{n}.{july} \\ $$$$\:\:\:\:\:\:\:\:\:...\clubsuit{m}.{n}.{july}.\mathrm{1970}\clubsuit... \\ $$

Question Number 115273 Answers: 2 Comments: 0

... advanced mathematics... evaluate::: Δ=∫_0 ^( ∞) ((cos(ln(x)))/((x+1)^2 )) dx =??? ...m.n.july.1970...

$$\:\:\:\:\:\:\:\:...\:{advanced}\:\:{mathematics}... \\ $$$$ \\ $$$$\:\:\:\:\:{evaluate}::: \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Delta=\int_{\mathrm{0}} ^{\:\infty} \:\frac{{cos}\left({ln}\left({x}\right)\right)}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }\:{dx}\:=??? \\ $$$$ \\ $$$$\:\:\:\:\:\:\:...{m}.{n}.{july}.\mathrm{1970}... \\ $$$$\: \\ $$

Question Number 115268 Answers: 1 Comments: 0

(√(4^x −5.2^(x+1) +25)) +(√(9^x −2.3^(x+2) +17)) ≤ 2^x −5

$$\sqrt{\mathrm{4}^{{x}} −\mathrm{5}.\mathrm{2}^{{x}+\mathrm{1}} +\mathrm{25}}\:+\sqrt{\mathrm{9}^{{x}} −\mathrm{2}.\mathrm{3}^{{x}+\mathrm{2}} +\mathrm{17}}\:\leqslant\:\mathrm{2}^{{x}} −\mathrm{5} \\ $$

Question Number 115267 Answers: 1 Comments: 0

If f(x) is a differentiable function defined ∀x∈R such that (f(x))^3 −x+f(x)=0 then ∫_0 ^(√2) f^(−1) (x) dx =

$${If}\:{f}\left({x}\right)\:{is}\:{a}\:{differentiable}\:{function} \\ $$$${defined}\:\:\forall{x}\in\mathbb{R}\:{such}\:{that}\:\left({f}\left({x}\right)\right)^{\mathrm{3}} −{x}+{f}\left({x}\right)=\mathrm{0} \\ $$$${then}\:\underset{\mathrm{0}} {\overset{\sqrt{\mathrm{2}}} {\int}}\:{f}^{−\mathrm{1}} \left({x}\right)\:{dx}\:=\: \\ $$

Question Number 115261 Answers: 2 Comments: 0

Equation of circle touching the line ∣x−2∣+∣y−3∣ = 4 will be

$${Equation}\:{of}\:{circle}\:{touching}\:{the}\:{line}\: \\ $$$$\mid{x}−\mathrm{2}\mid+\mid{y}−\mathrm{3}\mid\:=\:\mathrm{4}\:{will}\:{be}\: \\ $$

Question Number 115260 Answers: 2 Comments: 1

Let f be a real valued function defined on the interval (−1,1) such that e^(−x) .f(x)=2+∫_0 ^x (√(t^4 +1)) dt ∀x∈(−1,1) and let g be the inverse function of f . Find the value of g′(2).

$${Let}\:{f}\:{be}\:{a}\:{real}\:{valued}\:{function}\:{defined} \\ $$$${on}\:{the}\:{interval}\:\left(−\mathrm{1},\mathrm{1}\right)\:{such}\:{that}\: \\ $$$${e}^{−{x}} .{f}\left({x}\right)=\mathrm{2}+\underset{\mathrm{0}} {\overset{{x}} {\int}}\:\sqrt{{t}^{\mathrm{4}} +\mathrm{1}}\:{dt}\:\forall{x}\in\left(−\mathrm{1},\mathrm{1}\right) \\ $$$${and}\:{let}\:{g}\:{be}\:{the}\:{inverse}\:{function}\:{of}\:{f} \\ $$$$.\:{Find}\:{the}\:{value}\:{of}\:{g}'\left(\mathrm{2}\right). \\ $$

Question Number 115258 Answers: 1 Comments: 0

A vector of magnitude 2 along a bisector of the angle between the two vectors 2i^ −2j^ +k^ and i^ +2j^ −2k^ is __

$${A}\:{vector}\:{of}\:{magnitude}\:\mathrm{2}\:{along}\:{a}\:{bisector} \\ $$$${of}\:{the}\:{angle}\:{between}\:{the}\:{two}\:{vectors} \\ $$$$\mathrm{2}\hat {{i}}−\mathrm{2}\hat {{j}}+\hat {{k}}\:{and}\:\hat {{i}}+\mathrm{2}\hat {{j}}−\mathrm{2}\hat {{k}}\:{is}\:\_\_ \\ $$

Question Number 115255 Answers: 0 Comments: 0

Express cosec 3x in terms of cosec x.

$$\mathrm{Express}\:\mathrm{cosec}\:\mathrm{3x}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{cosec}\:\mathrm{x}. \\ $$

Question Number 115253 Answers: 1 Comments: 0

Express sin 4x interm of sin x.

$$\mathrm{Express}\:\mathrm{sin}\:\mathrm{4x}\:\mathrm{interm}\:\mathrm{of}\:\mathrm{sin}\:\mathrm{x}. \\ $$

Question Number 115250 Answers: 0 Comments: 0

If mr Fosu sells the car after covering a mileage of 128km. find the i. value of the car if the rate of depreciation is $ 0.03 per km ii. the range of values for which Mr Fosu could sell the car so that he does not lose more than $,2000 or gain more tban $3,000 on the depreciated value.

$$\mathrm{If}\:\mathrm{mr}\:\mathrm{Fosu}\:\mathrm{sells}\:\mathrm{the}\:\mathrm{car}\:\mathrm{after}\:\mathrm{covering}\: \\ $$$$\mathrm{a}\:\mathrm{mileage}\:\mathrm{of}\:\mathrm{128km}.\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\mathrm{i}.\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{car}\:\mathrm{if}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{of}\: \\ $$$$\mathrm{depreciation}\:\mathrm{is}\:\$\:\mathrm{0}.\mathrm{03}\:\mathrm{per}\:\mathrm{km} \\ $$$$\mathrm{ii}.\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{values}\:\mathrm{for}\:\mathrm{which}\:\mathrm{Mr} \\ $$$$\mathrm{Fosu}\:\mathrm{could}\:\mathrm{sell}\:\mathrm{the}\:\mathrm{car}\:\mathrm{so}\:\mathrm{that}\:\mathrm{he}\:\mathrm{does} \\ $$$$\mathrm{not}\:\mathrm{lose}\:\mathrm{more}\:\mathrm{than}\:\$,\mathrm{2000}\:\mathrm{or}\:\mathrm{gain}\:\mathrm{more}\:\mathrm{tban}\: \\ $$$$\$\mathrm{3},\mathrm{000}\:\mathrm{on}\:\mathrm{the}\:\mathrm{depreciated}\:\mathrm{value}. \\ $$

Question Number 115248 Answers: 1 Comments: 0

Express cos 4x interm of cos x.

$$\mathrm{Express}\:\mathrm{cos}\:\mathrm{4x}\:\mathrm{interm}\:\mathrm{of}\:\mathrm{cos}\:\mathrm{x}. \\ $$

Question Number 115246 Answers: 0 Comments: 1

5^((x+1)^2 ) + 625 ≤ 5^(x^2 +2) + 5^(2x+3)

$$\:\:\:\:\mathrm{5}^{\left({x}+\mathrm{1}\right)^{\mathrm{2}} } \:+\:\mathrm{625}\:\leqslant\:\mathrm{5}^{{x}^{\mathrm{2}} +\mathrm{2}} \:+\:\mathrm{5}^{\mathrm{2}{x}+\mathrm{3}} \\ $$

Question Number 115238 Answers: 2 Comments: 0

64^(x^2 −(3/4)x) ≤ ((√8))^x^3

$$\:\:\:\mathrm{64}^{{x}^{\mathrm{2}} −\frac{\mathrm{3}}{\mathrm{4}}{x}} \:\leqslant\:\left(\sqrt{\mathrm{8}}\right)^{{x}^{\mathrm{3}} } \: \\ $$

Question Number 115237 Answers: 2 Comments: 0

Question Number 115230 Answers: 0 Comments: 6

2 women and 4 men will sit on the 8 available seats and surround the round table . The many possible arrangements of them sitting if they sat randomly

$$\mathrm{2}\:{women}\:{and}\:\mathrm{4}\:{men}\:{will}\:{sit}\:{on}\:{the} \\ $$$$\mathrm{8}\:{available}\:{seats}\:{and}\:{surround}\: \\ $$$${the}\:{round}\:{table}\:.\:{The}\:{many}\:{possible} \\ $$$${arrangements}\:{of}\:{them}\:{sitting} \\ $$$${if}\:{they}\:{sat}\:{randomly} \\ $$

Question Number 115229 Answers: 2 Comments: 0

find the mean value of y=(5/(2−x−3x^2 )) between x=−(1/3) and x=(1/3)

$${find}\:{the}\:{mean}\:{value}\:{of}\: \\ $$$${y}=\frac{\mathrm{5}}{\mathrm{2}−{x}−\mathrm{3}{x}^{\mathrm{2}} }\:\:{between}\:{x}=−\frac{\mathrm{1}}{\mathrm{3}}\:{and} \\ $$$${x}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$

Question Number 115222 Answers: 1 Comments: 0

.... nice math ... nice integral prove :: Ψ=9∫_0 ^( ∞) x^5 e^(−x^3 ) ln(1+x)dx =^(???) Γ((1/3))−Γ((2/3))+Γ((3/3)) m.n.july.1970

$$\:\:\:\:\:\:....\:{nice}\:\:{math}\:... \\ $$$$ \\ $$$$\:\:\:\:{nice}\:\:{integral}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{prove}\::: \\ $$$$\Psi=\mathrm{9}\int_{\mathrm{0}} ^{\:\infty} {x}^{\mathrm{5}} {e}^{−{x}^{\mathrm{3}} } {ln}\left(\mathrm{1}+{x}\right){dx}\:\overset{???} {=}\:\Gamma\left(\frac{\mathrm{1}}{\mathrm{3}}\right)−\Gamma\left(\frac{\mathrm{2}}{\mathrm{3}}\right)+\Gamma\left(\frac{\mathrm{3}}{\mathrm{3}}\right)\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{m}.{n}.{july}.\mathrm{1970} \\ $$$$\:\: \\ $$

Question Number 115215 Answers: 2 Comments: 7

solve ∫_0 ^1 ln^2 (1−x^2 )dx

$${solve} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}^{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 115224 Answers: 2 Comments: 0