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Question Number 74484 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((arctan(2x))/(x^2 +3))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{{x}^{\mathrm{2}} +\mathrm{3}}{dx} \\ $$

Question Number 74483 Answers: 1 Comments: 2

Question Number 74446 Answers: 1 Comments: 0

Question Number 74431 Answers: 0 Comments: 11

Question Number 74429 Answers: 0 Comments: 2

Question Number 74455 Answers: 1 Comments: 0

if K=(x∈R 2x−1+∣2x−1∣=0 )and J=(x∈R −x(2x+1)≤−1) find J−K.

$${if}\:{K}=\left({x}\in\mathbb{R}\:\mathrm{2}{x}−\mathrm{1}+\mid\mathrm{2}{x}−\mathrm{1}\mid=\mathrm{0}\:\right){and} \\ $$$${J}=\left({x}\in\mathbb{R}\:−{x}\left(\mathrm{2}{x}+\mathrm{1}\right)\leqslant−\mathrm{1}\right)\:{find}\:{J}−{K}. \\ $$

Question Number 74423 Answers: 0 Comments: 1

Question Number 74419 Answers: 0 Comments: 1

Question Number 74418 Answers: 1 Comments: 0

Question Number 74415 Answers: 1 Comments: 1

Question Number 74412 Answers: 0 Comments: 0

a,b,c are given real constants. p,q,r,t are unknowns from which we can choose values of two of them (non zero) and have to determine the other two (non zero), obeying two equations given below p^2 +q(1+bq)t^2 +q(ap+br)t +r(1+bq)t+r(ap+br) = 0 pt+q(a+cq)t^2 +r(a+cq)t +cqrt+cr^2 = 0 Can this be done solving a quadratic eq. and none higher..?

$${a},{b},{c}\:{are}\:{given}\:{real}\:{constants}. \\ $$$${p},{q},{r},{t}\:{are}\:{unknowns}\:{from}\:{which} \\ $$$${we}\:{can}\:{choose}\:{values}\:{of}\:{two}\:{of} \\ $$$${them}\:\left({non}\:{zero}\right)\:{and}\:{have}\:{to}\: \\ $$$${determine}\:{the}\:{other}\:{two}\:\left({non}\:{zero}\right), \\ $$$${obeying}\:\:{two}\:{equations}\:{given}\:{below} \\ $$$$\:{p}^{\mathrm{2}} +{q}\left(\mathrm{1}+{bq}\right){t}^{\mathrm{2}} +{q}\left({ap}+{br}\right){t} \\ $$$$\:\:\:\:\:+{r}\left(\mathrm{1}+{bq}\right){t}+{r}\left({ap}+{br}\right)\:=\:\mathrm{0} \\ $$$${pt}+{q}\left({a}+{cq}\right){t}^{\mathrm{2}} +{r}\left({a}+{cq}\right){t} \\ $$$$\:\:\:\:+{cqrt}+{cr}^{\mathrm{2}} =\:\mathrm{0} \\ $$$${Can}\:{this}\:{be}\:{done}\:{solving}\:{a} \\ $$$${quadratic}\:{eq}.\:{and}\:{none}\:{higher}..? \\ $$

Question Number 74411 Answers: 1 Comments: 0

A rocket vertically from the surface of the earth with an initil velocity(v_o ) show that its velocity v at height h is given by v_o ^2 −v^2 =((2gh)/(1+(h/R))) where R is radius of earth and g is the acceleration due to gravity at the earth surface

$${A}\:{rocket}\:{vertically}\:{from} \\ $$$${the}\:{surface}\:{of}\:{the}\:{earth} \\ $$$${with}\:{an}\:{initil}\:{velocity}\left({v}_{{o}} \right) \\ $$$${show}\:{that}\:{its}\:{velocity}\:{v} \\ $$$${at}\:{height}\:{h}\:{is}\:{given}\:{by} \\ $$$${v}_{{o}} ^{\mathrm{2}} −{v}^{\mathrm{2}} =\frac{\mathrm{2}{gh}}{\mathrm{1}+\frac{{h}}{{R}}} \\ $$$${where}\:{R}\:{is}\:{radius}\:{of}\:{earth} \\ $$$${and}\:\:{g}\:{is}\:{the}\:{acceleration} \\ $$$${due}\:{to}\:{gravity}\:{at}\:{the}\:{earth} \\ $$$${surface} \\ $$

Question Number 75089 Answers: 0 Comments: 4

∫sin (x^3 +c) dx=? ∫sinh (x^3 +c) dx=?

$$\int\mathrm{sin}\:\left({x}^{\mathrm{3}} +{c}\right)\:{dx}=? \\ $$$$\int\mathrm{sinh}\:\left({x}^{\mathrm{3}} +{c}\right)\:{dx}=? \\ $$

Question Number 74509 Answers: 0 Comments: 4

Question Number 74386 Answers: 0 Comments: 0

z(x)=u(x)+v(x)=Z(K)=U(K)+V(K) f u(x)=Σ(1/(k!)) (d^ k/(dx^ k))(x−xo)

$$\mathrm{z}\left(\mathrm{x}\right)=\mathrm{u}\left(\mathrm{x}\right)+\mathrm{v}\left(\mathrm{x}\right)=\mathrm{Z}\left(\mathrm{K}\right)=\mathrm{U}\left(\mathrm{K}\right)+\mathrm{V}\left(\mathrm{K}\right) \\ $$$$\mathrm{f}\:\mathrm{u}\left(\mathrm{x}\right)=\Sigma\frac{\mathrm{1}}{\mathrm{k}!}\:\frac{\hat {\mathrm{d}k}}{\mathrm{d}\hat {\mathrm{x}k}}\left(\mathrm{x}−\mathrm{x}{o}\right) \\ $$

Question Number 74384 Answers: 1 Comments: 1

Question Number 74383 Answers: 0 Comments: 3

Question Number 74369 Answers: 0 Comments: 0

please state Cramer′s rule

$${please}\:{state}\:{Cramer}'{s}\:{rule} \\ $$

Question Number 74394 Answers: 1 Comments: 4

Question Number 74367 Answers: 0 Comments: 2

Solve : (D^4 +4)y=0 given: y(0)=0 , y′(0)=2 , y′′(0)=0 and y′′′(0)=4.

$${Solve}\:: \\ $$$$\left({D}^{\mathrm{4}} +\mathrm{4}\right){y}=\mathrm{0}\: \\ $$$${given}:\:{y}\left(\mathrm{0}\right)=\mathrm{0}\:,\:{y}'\left(\mathrm{0}\right)=\mathrm{2}\:,\:{y}''\left(\mathrm{0}\right)=\mathrm{0}\:{and} \\ $$$${y}'''\left(\mathrm{0}\right)=\mathrm{4}. \\ $$

Question Number 74355 Answers: 1 Comments: 0

let f(x), g(x) and h(x) be functions R→R, given by f(x)=x^2 , if x≥0 and x+1 if x<0 g(x)=x^2 −4, if x≥2 and (1/(2−x)) if x<2 h(x)=3^(−x) , if x≤0 and 3^x if x≥0 Calculate ((f(2)+f(g(2)))/(f(g(h(−1))))).

$${let}\:{f}\left({x}\right),\:{g}\left({x}\right)\:{and}\:{h}\left({x}\right)\:{be}\:{functions} \\ $$$$\mathbb{R}\rightarrow\mathbb{R},\:{given}\:{by} \\ $$$${f}\left({x}\right)={x}^{\mathrm{2}} ,\:{if}\:{x}\geqslant\mathrm{0}\:{and}\:{x}+\mathrm{1}\:{if}\:{x}<\mathrm{0} \\ $$$${g}\left({x}\right)={x}^{\mathrm{2}} −\mathrm{4},\:{if}\:{x}\geqslant\mathrm{2}\:{and}\:\frac{\mathrm{1}}{\mathrm{2}−{x}}\:{if}\:{x}<\mathrm{2} \\ $$$${h}\left({x}\right)=\mathrm{3}^{−{x}} ,\:{if}\:{x}\leqslant\mathrm{0}\:{and}\:\mathrm{3}^{{x}} \:{if}\:{x}\geqslant\mathrm{0} \\ $$$${Calculate}\:\frac{{f}\left(\mathrm{2}\right)+{f}\left({g}\left(\mathrm{2}\right)\right)}{{f}\left({g}\left({h}\left(−\mathrm{1}\right)\right)\right)}. \\ $$

Question Number 74395 Answers: 0 Comments: 2

calculate ∫_0 ^∞ e^(−2x) [e^x ]dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:{e}^{−\mathrm{2}{x}} \left[{e}^{{x}} \right]{dx} \\ $$

Question Number 74353 Answers: 0 Comments: 0

let A_n =Σ_(k=0) ^n (1/(k+(√(k^2 +1)))) 1)find lim_(n→+∞) A_n 2) determine a equivalent of A_n when n→+∞

$${let}\:\:{A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\frac{\mathrm{1}}{{k}+\sqrt{{k}^{\mathrm{2}} +\mathrm{1}}} \\ $$$$\left.\mathrm{1}\right){find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{a}\:{equivalent}\:{of}\:{A}_{{n}} \:\:{when}\:{n}\rightarrow+\infty \\ $$$$ \\ $$

Question Number 74352 Answers: 1 Comments: 0

let U_n =Σ_(k=0) ^n (1/(k^2 +k+1)) find a equivalent of U_n (n→+∞)

$${let}\:{U}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\:\frac{\mathrm{1}}{{k}^{\mathrm{2}} +{k}+\mathrm{1}}\:\:{find}\:{a}\:{equivalent}\:{of}\:{U}_{{n}} \:\:\:\left({n}\rightarrow+\infty\right) \\ $$$$ \\ $$

Question Number 74351 Answers: 0 Comments: 1

find the value of Σ_(n=1) ^(+∞) (((−1)^n )/((4n^2 −1)^2 ))

$${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{+\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 74350 Answers: 0 Comments: 1

findf(a)= ∫_(−∞) ^(+∞) ((arctan(cosx))/(x^2 +a^2 ))dx witha>0

$${findf}\left({a}\right)=\:\int_{−\infty} ^{+\infty} \:\frac{{arctan}\left({cosx}\right)}{{x}^{\mathrm{2}} +{a}^{\mathrm{2}} }{dx}\:{witha}>\mathrm{0} \\ $$

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