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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 ))