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Question Number 38853 Answers: 0 Comments: 1

Question Number 39030 Answers: 2 Comments: 3

1) let f(x) = ∫_0 ^∞ (dt/(1+x^2 t^4 )) with x >0 find a simple form of f(x) 2) calculate ∫_0 ^(+∞) (dt/(1+t^4 )) 3) calculate ∫_0 ^∞ (dt/(1+3t^4 ))

$$\left.\mathrm{1}\right)\:{let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\mathrm{1}+{x}^{\mathrm{2}} {t}^{\mathrm{4}} }\:\:{with}\:{x}\:>\mathrm{0} \\ $$$${find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{4}} } \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dt}}{\mathrm{1}+\mathrm{3}{t}^{\mathrm{4}} } \\ $$

Question Number 38849 Answers: 1 Comments: 1

Question Number 38847 Answers: 0 Comments: 0

Question Number 38836 Answers: 0 Comments: 0

Question Number 38825 Answers: 1 Comments: 4

Question Number 38822 Answers: 1 Comments: 1

The incident wave set up on a string of length fixed at each end is given by: y_1 =Asin(kx−wt) i)what is the equation of motion of the reflected wave,y_2 . ii)obtain the resultant,y=y_1 +y_2 of the two waves. iii)what type of resultant wave is this? iv)for what values of x will the amplitud of the resultant wave become zero? v)for what values of x will y be maximum?

$${The}\:{incident}\:{wave}\:{set}\:{up}\:{on}\:{a}\:{string} \\ $$$${of}\:{length}\:{fixed}\:{at}\:{each}\:{end}\:{is}\:{given} \\ $$$${by}:\:\:\:{y}_{\mathrm{1}} ={Asin}\left({kx}−{wt}\right) \\ $$$$\left.{i}\right){what}\:{is}\:{the}\:{equation}\:{of}\:{motion} \\ $$$${of}\:{the}\:{reflected}\:{wave},{y}_{\mathrm{2}} . \\ $$$$\left.{ii}\right){obtain}\:{the}\:{resultant},{y}={y}_{\mathrm{1}} +{y}_{\mathrm{2}} \\ $$$${of}\:{the}\:{two}\:{waves}. \\ $$$$\left.{iii}\right){what}\:{type}\:{of}\:{resultant}\:{wave}\:{is} \\ $$$${this}? \\ $$$$\left.{iv}\right){for}\:{what}\:{values}\:{of}\:{x}\:{will}\:{the} \\ $$$${amplitud}\:{of}\:{the}\:{resultant}\:{wave}\: \\ $$$${become}\:{zero}? \\ $$$$\left.{v}\right){for}\:{what}\:{values}\:{of}\:{x}\:{will}\:{y}\:{be} \\ $$$${maximum}? \\ $$

Question Number 38816 Answers: 1 Comments: 0

Two waves are represented by y_1 =Asinωt and y_2 =Asin(ωt−δ). What is the resultant of the two waves? ii)determine the amplitude of the resultant wave and under which condition will it be constructive or destructive.

$${Two}\:{waves}\:{are}\:{represented}\:{by} \\ $$$${y}_{\mathrm{1}} ={Asin}\omega{t}\:{and}\:{y}_{\mathrm{2}} ={Asin}\left(\omega{t}−\delta\right). \\ $$$${What}\:{is}\:{the}\:{resultant}\:{of}\:{the}\:{two} \\ $$$${waves}? \\ $$$$\left.{ii}\right){determine}\:{the}\:{amplitude}\:{of}\:{the} \\ $$$${resultant}\:{wave}\:{and}\:{under}\:{which} \\ $$$${condition}\:{will}\:{it}\:{be}\:{constructive}\:{or} \\ $$$${destructive}. \\ $$

Question Number 38812 Answers: 0 Comments: 1

Can you remember this formula and the question behind it? 𝚽=mn−𝚺_(i=1) ^m 𝚺_(j=1) ^n sign[gcd(i,j)−1] The first prize goes to that one who can tell the # of the initial question.

$${Can}\:{you}\:{remember}\:{this}\:{formula}\:{and} \\ $$$${the}\:{question}\:{behind}\:{it}? \\ $$$$\:\:\:\:\boldsymbol{\Phi}=\boldsymbol{{mn}}−\underset{\boldsymbol{{i}}=\mathrm{1}} {\overset{\boldsymbol{{m}}} {\boldsymbol{\sum}}}\:\underset{\boldsymbol{{j}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\boldsymbol{\sum}}}\:\boldsymbol{{sign}}\left[\boldsymbol{{gcd}}\left(\boldsymbol{{i}},\boldsymbol{{j}}\right)−\mathrm{1}\right] \\ $$$${The}\:{first}\:{prize}\:{goes}\:{to}\:{that}\:{one}\:{who} \\ $$$${can}\:{tell}\:{the}\:#\:{of}\:{the}\:{initial}\:{question}. \\ $$

Question Number 38804 Answers: 1 Comments: 3

let A_n = ∫_0 ^n (((−1)^x )/(2[x] +1))dx 1) calculate A_n 2) find lim_(n→+∞) A_n

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

Question Number 38802 Answers: 2 Comments: 0

solve: y′′(1 + 4x^2 ) − 8y = 0

$$\mathrm{solve}:\:\:\:\mathrm{y}''\left(\mathrm{1}\:+\:\mathrm{4x}^{\mathrm{2}} \right)\:−\:\mathrm{8y}\:=\:\mathrm{0} \\ $$

Question Number 39029 Answers: 2 Comments: 0

∫((3−5(√(1−(1/x)))))^(1/3) dx=? ∫(1/((3−5(√(1−(1/x)))))^(1/3) )dx=?

$$\int\sqrt[{\mathrm{3}}]{\mathrm{3}−\mathrm{5}\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}}{dx}=? \\ $$$$\int\frac{\mathrm{1}}{\sqrt[{\mathrm{3}}]{\mathrm{3}−\mathrm{5}\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}}}{dx}=? \\ $$

Question Number 38786 Answers: 0 Comments: 5

Question Number 38775 Answers: 1 Comments: 2

Question Number 38765 Answers: 0 Comments: 10

App notification problem has been fixed. Please report if u are still not able to get notification. Issue was on server side so no app updates are needed.

$$\mathrm{App}\:\mathrm{notification}\:\mathrm{problem}\:\mathrm{has} \\ $$$$\mathrm{been}\:\mathrm{fixed}.\:\mathrm{Please}\:\mathrm{report}\:\mathrm{if}\:\mathrm{u}\:\mathrm{are} \\ $$$$\mathrm{still}\:\mathrm{not}\:\mathrm{able}\:\mathrm{to}\:\mathrm{get}\:\mathrm{notification}. \\ $$$$ \\ $$$$\mathrm{Issue}\:\mathrm{was}\:\mathrm{on}\:\mathrm{server}\:\mathrm{side}\:\mathrm{so}\:\mathrm{no}\:\mathrm{app} \\ $$$$\mathrm{updates}\:\mathrm{are}\:\mathrm{needed}. \\ $$

Question Number 38762 Answers: 2 Comments: 2

Question Number 38759 Answers: 0 Comments: 2

3+3=

$$\mathrm{3}+\mathrm{3}= \\ $$

Question Number 38746 Answers: 0 Comments: 3

this is still waiting to be solved... ∫((√((t−1)t(t+1)))/(3t^2 −4))dt=?

$$\mathrm{this}\:\mathrm{is}\:\mathrm{still}\:\mathrm{waiting}\:\mathrm{to}\:\mathrm{be}\:\mathrm{solved}... \\ $$$$\int\frac{\sqrt{\left({t}−\mathrm{1}\right){t}\left({t}+\mathrm{1}\right)}}{\mathrm{3}{t}^{\mathrm{2}} −\mathrm{4}}{dt}=? \\ $$

Question Number 38743 Answers: 1 Comments: 0

If sin θ + sin φ = a and cos θ + cos φ = b, find the value of tan ((θ−φ)/2)(in terms of a and b).

$$\mathrm{If}\:\mathrm{sin}\:\theta\:+\:{sin}\:\phi\:=\:{a}\:\mathrm{and}\:\mathrm{cos}\:\theta\:+\:\mathrm{cos}\:\phi\:=\:{b},\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{tan}\:\frac{\theta−\phi}{\mathrm{2}}\left({in}\:{terms}\:{of}\:{a}\:{and}\:{b}\right). \\ $$

Question Number 38741 Answers: 0 Comments: 1

7.2+[0.2 of 10−{0.6+0.3−0.8−0.6}]

$$\mathrm{7}.\mathrm{2}+\left[\mathrm{0}.\mathrm{2}\:{of}\:\mathrm{10}−\left\{\mathrm{0}.\mathrm{6}+\mathrm{0}.\mathrm{3}−\mathrm{0}.\mathrm{8}−\mathrm{0}.\mathrm{6}\right\}\right] \\ $$

Question Number 38740 Answers: 1 Comments: 4

find tbe polynom p withdegre 5 wich verify p(x+1)−p(x)=x^4 and p(0)=0 for that put p(x)=ax^5 +bx^4 +cx^3 +dx^2 +ex +f and find the coefficients. 2) find interms of n the value of sum 1 +2^4 +3^4 +....+n^4 .

$${find}\:{tbe}\:{polynom}\:{p}\:{withdegre}\:\mathrm{5}\:{wich}\:{verify} \\ $$$${p}\left({x}+\mathrm{1}\right)−{p}\left({x}\right)={x}^{\mathrm{4}} \:\:{and}\:{p}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$${for}\:{that}\:{put}\:{p}\left({x}\right)={ax}^{\mathrm{5}} \:+{bx}^{\mathrm{4}} \:+{cx}^{\mathrm{3}} \:+{dx}^{\mathrm{2}} \\ $$$$+{ex}\:+{f}\:\:{and}\:{find}\:{the}\:{coefficients}. \\ $$$$\left.\mathrm{2}\right)\:{find}\:{interms}\:{of}\:{n}\:{the}\:{value}\:{of} \\ $$$${sum}\:\mathrm{1}\:+\mathrm{2}^{\mathrm{4}} \:+\mathrm{3}^{\mathrm{4}} +....+{n}^{\mathrm{4}} \:. \\ $$

Question Number 38734 Answers: 0 Comments: 1

Find the domain of the function f (x) = 1 − cos^2 x

$${Find}\:{the}\:{domain}\:{of}\:{the}\:{function} \\ $$$${f}\:\left({x}\right)\:=\:\mathrm{1}\:−\:{cos}^{\mathrm{2}} \:{x} \\ $$

Question Number 38731 Answers: 0 Comments: 1

Question Number 38728 Answers: 0 Comments: 1

find L ( (e^(−(x/a)) /a)) with a≠0 and L laplace transfom.

$${find}\:{L}\:\left(\:\frac{{e}^{−\frac{{x}}{{a}}} }{{a}}\right)\:\:{with}\:{a}\neq\mathrm{0}\:\:{and}\:{L}\:{laplace}\:{transfom}. \\ $$

Question Number 38727 Answers: 0 Comments: 2

let n from N and A_n = ∫_(−∞) ^(+∞) ((cos(ax))/((x^2 +x+1)^n ))dx and B_n = ∫_(−∞) ^(+∞) ((sin(ax))/((x^2 +x+1)^n ))dx find the value of A_(n ) and B_n .

$${let}\:{n}\:{from}\:{N}\:\:{and}\:\:{A}_{{n}} =\:\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{cos}\left({ax}\right)}{\left({x}^{\mathrm{2}} \:+{x}+\mathrm{1}\right)^{{n}} }{dx}\:\:{and} \\ $$$${B}_{{n}} =\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{sin}\left({ax}\right)}{\left({x}^{\mathrm{2}} \:+{x}+\mathrm{1}\right)^{{n}} }{dx} \\ $$$${find}\:{the}\:{value}\:{of}\:{A}_{{n}\:} \:\:{and}\:{B}_{{n}} \:\:. \\ $$$$ \\ $$

Question Number 38726 Answers: 0 Comments: 1

let f(x)=((x+1)/(2 +e^(−2x) )) developp f at integr serie.

$${let}\:{f}\left({x}\right)=\frac{{x}+\mathrm{1}}{\mathrm{2}\:+{e}^{−\mathrm{2}{x}} }\:\:\:{developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$

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