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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

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

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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

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

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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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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.

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

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