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A force F = 2t i + 5j acts on a particle of mass 2kg. find the velocity and the magnitude of the impulse that acts on the particle within the time range 1s ≤ t ≤ 3s

$${A}\:{force}\:{F}\:=\:\mathrm{2}{t}\:\boldsymbol{{i}}\:+\:\mathrm{5}\boldsymbol{{j}}\:{acts}\:{on} \\ $$$${a}\:{particle}\:{of}\:{mass}\:\mathrm{2}{kg}.\:{find} \\ $$$${the}\:{velocity}\:{and}\:{the}\:{magnitude} \\ $$$${of}\:{the}\:{impulse}\:{that}\:{acts}\:{on}\: \\ $$$${the}\:{particle}\:{within}\:{the}\:{time} \\ $$$${range}\:\:\mathrm{1}\boldsymbol{{s}}\:\leqslant\:\boldsymbol{{t}}\:\leqslant\:\mathrm{3}\boldsymbol{{s}} \\ $$

Question Number 39755 Answers: 1 Comments: 0

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calculate ∫_(−∞) ^(+∞) ((cos(x^n ) +sin(x^n ))/((x^2 +9)^n )) dx

$${calculate}\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{cos}\left({x}^{{n}} \right)\:+{sin}\left({x}^{{n}} \right)}{\left({x}^{\mathrm{2}} \:+\mathrm{9}\right)^{{n}} }\:{dx} \\ $$

Question Number 39711 Answers: 0 Comments: 1

calculate ∫_(−∞) ^(+∞) (x^n /((1+x^2 )^n )) dx with n natral integr

$${calculate}\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{x}^{{n}} }{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} }\:{dx}\:{with}\:{n}\:{natral}\:{integr} \\ $$

Question Number 39709 Answers: 1 Comments: 1

Question Number 39708 Answers: 1 Comments: 0

Find the complex number z if arg(z+1)=(π/3) arg(z−1)=((4π)/3)

$${Find}\:{the}\:{complex}\:{number}\:{z}\:{if} \\ $$$${arg}\left({z}+\mathrm{1}\right)=\frac{\pi}{\mathrm{3}} \\ $$$${arg}\left({z}−\mathrm{1}\right)=\frac{\mathrm{4}\pi}{\mathrm{3}} \\ $$

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Question Number 39703 Answers: 0 Comments: 1

let A_n = ∫_0 ^n (((−1)^([x]) )/(x+2−[x]))dx 1) calculate A_n and lim_(n→+∞) A_n 2) let S_n =Σ_(n=0) ^n A_n dtudy the convergence of S_n 4) let W_n = Σ_(n=1) ^n (1/A_n ) study the convergence of W_n

$${let}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \:\:\:\frac{\left(−\mathrm{1}\right)^{\left[{x}\right]} }{{x}+\mathrm{2}−\left[{x}\right]}{dx} \\ $$$$\left.\mathrm{1}\right)\:\:{calculate}\:{A}_{{n}} \:\:\:{and}\:{lim}_{{n}\rightarrow+\infty} \:\:{A}_{{n}} \: \\ $$$$\left.\mathrm{2}\right)\:{let}\:{S}_{{n}} \:=\sum_{{n}=\mathrm{0}} ^{{n}} \:\:{A}_{{n}} \:\:\:{dtudy}\:{the}\:{convergence}\:{of}\:{S}_{{n}} \\ $$$$\left.\mathrm{4}\right)\:{let}\:\:{W}_{{n}} =\:\sum_{{n}=\mathrm{1}} ^{{n}} \:\:\frac{\mathrm{1}}{{A}_{{n}} } \\ $$$${study}\:{the}\:{convergence}\:{of}\:{W}_{{n}} \\ $$

Question Number 39702 Answers: 0 Comments: 6

let f(x)=2(√(x−(√(x−3)) +2)) 1) find D_f 2) calculate f^′ (x) 3) determine f^(−1) (x) 4) calculate (f^(−1) )^′ (x) 5) let u(x)=x^(2 ) +4 determine v(x)=fou(x) and calculate v^′ (x) 6)calculate ∫_3 ^5 f(x)dx.

$${let}\:{f}\left({x}\right)=\mathrm{2}\sqrt{{x}−\sqrt{{x}−\mathrm{3}}\:+\mathrm{2}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{determine}\:{f}^{−\mathrm{1}} \left({x}\right) \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\left({f}^{−\mathrm{1}} \right)^{'} \left({x}\right) \\ $$$$\left.\mathrm{5}\right)\:{let}\:{u}\left({x}\right)={x}^{\mathrm{2}\:} \:+\mathrm{4} \\ $$$${determine}\:\:{v}\left({x}\right)={fou}\left({x}\right)\:{and}\:{calculate} \\ $$$${v}^{'} \left({x}\right)\: \\ $$$$\left.\mathrm{6}\right){calculate}\:\:\int_{\mathrm{3}} ^{\mathrm{5}} \:{f}\left({x}\right){dx}. \\ $$

Question Number 39700 Answers: 0 Comments: 1

given that f(x)= x^3 − 3x^2 + ax + b and (x−1) is a factor of f(x) also the maximum value of f(x) at poin where x = 1 is 12 find a) (dy/d) (f(x)) b) the values of a and b c) factorise f(x) completely d) hence evaluate ∫_3 ^4 [f(x)] dx

$${given}\:{that}\:{f}\left({x}\right)=\:{x}^{\mathrm{3}} \:−\:\mathrm{3}{x}^{\mathrm{2}} \:+\:{ax}\:+\:{b} \\ $$$${and}\:\left({x}−\mathrm{1}\right)\:{is}\:{a}\:{factor}\:{of}\:{f}\left({x}\right) \\ $$$${also}\:{the}\:{maximum}\:{value}\:{of} \\ $$$${f}\left({x}\right)\:{at}\:{poin}\:{where}\:{x}\:=\:\mathrm{1} \\ $$$${is}\:\mathrm{12}\:{find}\: \\ $$$$\left.{a}\right)\:\frac{{dy}}{{d}}\:\left({f}\left({x}\right)\right) \\ $$$$\left.{b}\right)\:{the}\:{values}\:{of}\:{a}\:{and}\:{b} \\ $$$$\left.{c}\right)\:{factorise}\:{f}\left({x}\right)\:{completely} \\ $$$$\left.{d}\right)\:{hence}\:{evaluate}\:\int_{\mathrm{3}} ^{\mathrm{4}} \left[{f}\left({x}\right)\right]\:{dx} \\ $$

Question Number 39699 Answers: 0 Comments: 5

let f(x)= arctan(2x^2 +1) 1) calculate f^((n)) (x) 2) determine f^((n)) (n) 3)developp f at integr serie 4) calculate ∫_0 ^1 f(x)dx 5) calculate ∫_0 ^1 ((x arctan(2x^2 +1))/(2x^2 +2x +1))dx

$${let}\:{f}\left({x}\right)=\:{arctan}\left(\mathrm{2}{x}^{\mathrm{2}} \:+\mathrm{1}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{f}^{\left({n}\right)} \left({n}\right) \\ $$$$\left.\mathrm{3}\right){developp}\:{f}\:\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx} \\ $$$$\left.\mathrm{5}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{x}\:{arctan}\left(\mathrm{2}{x}^{\mathrm{2}} \:+\mathrm{1}\right)}{\mathrm{2}{x}^{\mathrm{2}} \:+\mathrm{2}{x}\:+\mathrm{1}}{dx} \\ $$

Question Number 39696 Answers: 1 Comments: 3

Question Number 39695 Answers: 0 Comments: 4

let f(x)=ln(2xarctan(√(2x^2 −1))) 1) find D_f 2)calculate f^′ (x) and determine its sign. 3) determine the equation of assymptote at pont A(1,f(1)) 3) find a and b from R / f(x)∼ a(x−1) +b (x→1) 4) calculate ∫_0 ^1 f(x)dx 5) calculate f^(′′) (x)

$${let}\:{f}\left({x}\right)={ln}\left(\mathrm{2}{xarctan}\sqrt{\left.\mathrm{2}{x}^{\mathrm{2}} \:−\mathrm{1}\right)}\right. \\ $$$$\left.\mathrm{1}\right)\:{find}\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right){calculate}\:{f}^{'} \left({x}\right)\:{and}\:\:{determine}\:{its}\:{sign}. \\ $$$$\left.\mathrm{3}\right)\:{determine}\:{the}\:{equation}\:{of}\:{assymptote}\:{at}\:{pont}\:{A}\left(\mathrm{1},{f}\left(\mathrm{1}\right)\right) \\ $$$$\left.\mathrm{3}\right)\:{find}\:{a}\:{and}\:{b}\:{from}\:{R}\:/\:\:{f}\left({x}\right)\sim\:{a}\left({x}−\mathrm{1}\right)\:+{b}\:\:\left({x}\rightarrow\mathrm{1}\right) \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{f}\left({x}\right){dx} \\ $$$$\left.\mathrm{5}\right)\:{calculate}\:{f}^{''} \left({x}\right) \\ $$

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