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let give I_(m,a) =∫_0 ^∞ ((cos(mx))/((1+x^2 )(x^2 +a^2 )))dx 1)verify that I_(m,1) =lim_(a→1) I_(m,a) 2) find the value of ∫_0 ^∞ ((x sin(mx))/((1+x^2 )^2 ))dx

$${let}\:{give}\:{I}_{{m},{a}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{cos}\left({mx}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)}{dx} \\ $$$$\left.\mathrm{1}\right){verify}\:{that}\:{I}_{{m},\mathrm{1}} ={lim}_{{a}\rightarrow\mathrm{1}} \:{I}_{{m},{a}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}\:{sin}\left({mx}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$

Question Number 28984 Answers: 0 Comments: 0

find F( (1/(1+x^4 ))) F means fourier transform.

$${find}\:{F}\left(\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{4}} }\right)\:{F}\:{means}\:{fourier}\:{transform}. \\ $$

Question Number 28983 Answers: 0 Comments: 0

find the value of∫_(−∞) ^(+∞) ((x^2 −1)/(x^2 +1)) ((sinx)/x)dx.

$${find}\:{the}\:{value}\:{of}\int_{−\infty} ^{+\infty} \:\frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}\:\frac{{sinx}}{{x}}{dx}. \\ $$

Question Number 28982 Answers: 0 Comments: 0

fnd the value of Π_(n=1) ^∞ ((n^2 +1)/n^2 ) .

$${fnd}\:{the}\:{value}\:{of}\:\prod_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{{n}^{\mathrm{2}} +\mathrm{1}}{{n}^{\mathrm{2}} }\:\:. \\ $$

Question Number 28981 Answers: 1 Comments: 1

find the values of Π_(n=2) ^∞ (1−(2/(n(n+1)))) .

$${find}\:{the}\:{values}\:{of}\:\prod_{{n}=\mathrm{2}} ^{\infty} \left(\mathrm{1}−\frac{\mathrm{2}}{{n}\left({n}+\mathrm{1}\right)}\right)\:. \\ $$

Question Number 28980 Answers: 0 Comments: 0

prove that sin(πz)=πz Π_(k=1) ^∞ (1−(z^2 /k^2 )) zfromC.

$${prove}\:{that}\:{sin}\left(\pi{z}\right)=\pi{z}\:\prod_{{k}=\mathrm{1}} ^{\infty} \left(\mathrm{1}−\frac{{z}^{\mathrm{2}} }{{k}^{\mathrm{2}} }\right)\:\:{zfromC}. \\ $$

Question Number 29012 Answers: 0 Comments: 1

Question Number 28978 Answers: 0 Comments: 0

let give p from R study the convergence of Π_(k=1) ^∞ (1+k^(−p) ) .

$${let}\:{give}\:{p}\:{from}\:{R}\:{study}\:{the}\:{convergence}\:{of} \\ $$$$\prod_{{k}=\mathrm{1}} ^{\infty} \:\left(\mathrm{1}+{k}^{−{p}} \right)\:. \\ $$

Question Number 28977 Answers: 0 Comments: 0

let give u_n =Σ_(k=1) ^n a_k ^2 with (a_k ) sequence of reals/a_(k>0) and v_n =Σ_(k=1) ^n (a_k /k) . prove that u_n converges⇒(v_n )converges

$${let}\:{give}\:{u}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:{a}_{{k}} ^{\mathrm{2}} \:\:\:\:\:{with}\:\left({a}_{{k}} \right)\:{sequence}\:{of}\:{reals}/{a}_{{k}>\mathrm{0}} \\ $$$${and}\:{v}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{{a}_{{k}} }{{k}}\:.\:{prove}\:{that}\:{u}_{{n}} {converges}\Rightarrow\left({v}_{{n}} \right){converges} \\ $$

Question Number 28976 Answers: 0 Comments: 0

find ∫_(−∞) ^(+∞) ((cosx)/(e^x +e^(−x) ))dx.

$${find}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{cosx}}{{e}^{{x}} +{e}^{−{x}} }{dx}. \\ $$

Question Number 28975 Answers: 0 Comments: 0

find the value of∫_0 ^∞ (x^3 /(1+x^7 ))dx.

$${find}\:{the}\:{value}\:{of}\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{\mathrm{3}} }{\mathrm{1}+{x}^{\mathrm{7}} }{dx}. \\ $$

Question Number 28960 Answers: 1 Comments: 1

Question Number 28954 Answers: 0 Comments: 0

please solve 4,5,6

$${please}\:{solve}\:\mathrm{4},\mathrm{5},\mathrm{6} \\ $$$$ \\ $$

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