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Operation ResearchQuestion and Answers: Page 1

Question Number 204469 Answers: 1 Comments: 0

Given the function f(x) = { ((2, 0< x <2)),((−2, −2 <x < 0)) :} of period 4 (a) sketch the graph of y = f(x) , for −6 < x < 6 (b) Find the Fourier coefficient a_0 , a_n , and b_n (c) write down the Fourier series. (d) hence show that Σ_(n=1) ^∞ (((−1)^n )/(2n−1)) = (π/4)

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{function}\:{f}\left({x}\right)\:=\:\begin{cases}{\mathrm{2},\:\mathrm{0}<\:{x}\:<\mathrm{2}}\\{−\mathrm{2},\:−\mathrm{2}\:<{x}\:<\:\mathrm{0}}\end{cases} \\ $$$$\mathrm{of}\:\mathrm{period}\:\mathrm{4} \\ $$$$\left(\mathrm{a}\right)\:\:\mathrm{sketch}\:\mathrm{the}\:\mathrm{graph}\:\mathrm{of}\:{y}\:=\:{f}\left({x}\right)\:,\:\mathrm{for}\:−\mathrm{6}\:<\:{x}\:<\:\mathrm{6} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{Fourier}\:\mathrm{coefficient}\:{a}_{\mathrm{0}} ,\:{a}_{{n}} ,\:\mathrm{and}\:{b}_{{n}} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{write}\:\mathrm{down}\:\mathrm{the}\:\mathrm{Fourier}\:\mathrm{series}.\: \\ $$$$\left(\mathrm{d}\right)\:\mathrm{hence}\:\mathrm{show}\:\mathrm{that}\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{2}{n}−\mathrm{1}}\:=\:\frac{\pi}{\mathrm{4}} \\ $$

Question Number 204104 Answers: 0 Comments: 0

Question Number 182854 Answers: 0 Comments: 7

(sin54)^(10) =x_1 x_(1 ) is root ax^2 +bx+c=0 a,b,c is integer a=?

$$\left({sin}\mathrm{54}\right)^{\mathrm{10}} ={x}_{\mathrm{1}} \:\:\:\:{x}_{\mathrm{1}\:\:} {is}\:{root} \\ $$$${ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$$\:\:{a},{b},{c}\:\:\:{is}\:{integer} \\ $$$${a}=? \\ $$

Question Number 182627 Answers: 1 Comments: 0

(((1+(√5))/2))^(15) =((a+b(√5))/2) find a+b

$$\left(\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\right)^{\mathrm{15}} =\frac{{a}+{b}\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$$${find}\:{a}+{b} \\ $$

Question Number 179857 Answers: 0 Comments: 1

Question Number 178653 Answers: 0 Comments: 0

Question Number 178652 Answers: 0 Comments: 0

calculer la branche infinie de(√(x^2 +2x+4))

$${calculer}\:{la}\:{branche}\:{infinie}\:{de}\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}} \\ $$

Question Number 178375 Answers: 1 Comments: 1

calculer une primitive de −3x/(√(x^2 +3))

$${calculer}\:{une}\:{primitive}\:{de}\:−\mathrm{3}{x}/\sqrt{{x}^{\mathrm{2}} +\mathrm{3}} \\ $$

Question Number 178349 Answers: 1 Comments: 0

etudier la fonction suivante 4x^3 −9x^2 +6x+1 calculer les limites puis dresser son tableau de variation

$${etudier}\:{la}\:{fonction}\:{suivante}\:\mathrm{4}{x}^{\mathrm{3}} −\mathrm{9}{x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{1} \\ $$$${calculer}\:{les}\:{limites}\:{puis}\:{dresser}\:{son}\:{tableau}\:{de}\:{variation} \\ $$

Question Number 176723 Answers: 0 Comments: 0

donner la forme trigonometrique(i−1)^5 /(i−4)^4

$${donner}\:{la}\:{forme}\:{trigonometrique}\left({i}−\mathrm{1}\right)^{\mathrm{5}} /\left({i}−\mathrm{4}\right)^{\mathrm{4}} \\ $$

Question Number 176719 Answers: 0 Comments: 0

Question Number 176549 Answers: 1 Comments: 0

donner la forme trigonometrique de 1/4(cosΠ/9+isinΠ/9)

$${donner}\:{la}\:{forme}\:{trigonometrique}\:{de}\:\mathrm{1}/\mathrm{4}\left({cos}\Pi/\mathrm{9}+{isin}\Pi/\mathrm{9}\right) \\ $$

Question Number 176379 Answers: 1 Comments: 0

lineariser sin^5 (x)

$${lineariser}\:{sin}^{\mathrm{5}} \left({x}\right) \\ $$

Question Number 176366 Answers: 1 Comments: 0

donner la forme trigonometrique de(1−i(√)3)(1+i)(cosθ−isinθ)

$${donner}\:{la}\:{forme}\:{trigonometrique}\:{de}\left(\mathrm{1}−{i}\sqrt{}\mathrm{3}\right)\left(\mathrm{1}+{i}\right)\left({cos}\theta−{isin}\theta\right) \\ $$

Question Number 176123 Answers: 0 Comments: 0

Question Number 176118 Answers: 0 Comments: 1

Question Number 176070 Answers: 0 Comments: 3

demontrer par recurrence que pour tout n>0 appartenent a l ensemble des entier naturel 3^(2n−2^(n ) ) est multiple de 7

$${demontrer}\:{par}\:{recurrence}\:{que}\:{pour}\:{tout}\:{n}>\mathrm{0}\:{appartenent}\:{a}\:{l}\:{ensemble}\:{des}\:{entier}\:{naturel}\:\mathrm{3}^{\mathrm{2}{n}−\mathrm{2}^{{n}\:} } {est}\:{multiple}\:{de}\:\mathrm{7} \\ $$

Question Number 176060 Answers: 2 Comments: 0

x^2 −4x+5=0

$${x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{5}=\mathrm{0} \\ $$

Question Number 176049 Answers: 1 Comments: 0

calculer (−1/2+i(√(3/2)^3 ))

$${calculer}\:\left(−\mathrm{1}/\mathrm{2}+{i}\sqrt{\left.\mathrm{3}/\mathrm{2}\right)^{\mathrm{3}} }\right. \\ $$

Question Number 176090 Answers: 2 Comments: 1

determiner z tel que z=z^2 −z+2

$${determiner}\:{z}\:{tel}\:{que}\:{z}={z}^{\mathrm{2}} −{z}+\mathrm{2} \\ $$$$ \\ $$

Question Number 175083 Answers: 0 Comments: 2

how the next number 1,2,5,9,6,13,8,17,....

$${how}\:{the}\:{next}\:{number}\:\mathrm{1},\mathrm{2},\mathrm{5},\mathrm{9},\mathrm{6},\mathrm{13},\mathrm{8},\mathrm{17},.... \\ $$

Question Number 181400 Answers: 0 Comments: 2

Question Number 154561 Answers: 1 Comments: 0

Question Number 144910 Answers: 0 Comments: 0

Γ(((n+1)/(1−i)))=????

$$\Gamma\left(\frac{{n}+\mathrm{1}}{\mathrm{1}−{i}}\right)=???? \\ $$

Question Number 140506 Answers: 2 Comments: 0

e^((((ζ(2))/2)−((ζ(3))/3)+((ζ(4))/4)−((ζ(5))/5)+...)) =?

$${e}^{\left(\frac{\zeta\left(\mathrm{2}\right)}{\mathrm{2}}−\frac{\zeta\left(\mathrm{3}\right)}{\mathrm{3}}+\frac{\zeta\left(\mathrm{4}\right)}{\mathrm{4}}−\frac{\zeta\left(\mathrm{5}\right)}{\mathrm{5}}+...\right)} \:\:\:=? \\ $$

Question Number 140487 Answers: 0 Comments: 0

∫_0 ^∞ ((1/( (√(1+x))))−(1/( (√(1+x^2 )))))(dx/x)=log(2)

$$\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}}}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\right)\frac{{dx}}{{x}}={log}\left(\mathrm{2}\right) \\ $$

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