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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

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

Question Number 28953 Answers: 0 Comments: 0

Question Number 28952 Answers: 0 Comments: 0

Question Number 28949 Answers: 0 Comments: 0

xy((x^4 −y^4 )/(x^4 +y^4 )) and 0 for origin then funtion is 1.continuous 2.mixpartial are not equal at origin 3.limit at origin is 1

$${xy}\frac{{x}^{\mathrm{4}} −{y}^{\mathrm{4}} }{{x}^{\mathrm{4}} +{y}^{\mathrm{4}} }\:\:{and}\:\mathrm{0}\:{for}\:{origin} \\ $$$${then}\:{funtion}\:{is} \\ $$$$\mathrm{1}.{continuous} \\ $$$$\mathrm{2}.{mixpartial}\:{are}\:{not}\:{equal}\:{at}\:{origin} \\ $$$$\mathrm{3}.{limit}\:{at}\:{origin}\:{is}\:\mathrm{1} \\ $$

Question Number 28938 Answers: 0 Comments: 3

Question Number 28932 Answers: 1 Comments: 0

Determine the least number of 4 digits, which is perfect square. Method of finding is required.

$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{least}\:\mathrm{number}\:\mathrm{of}\:\mathrm{4}\:\mathrm{digits}, \\ $$$$\mathrm{which}\:\mathrm{is}\:\mathrm{perfect}\:\mathrm{square}. \\ $$$$\mathrm{Method}\:\mathrm{of}\:\mathrm{finding}\:\mathrm{is}\:\boldsymbol{\mathrm{required}}. \\ $$

Question Number 28929 Answers: 1 Comments: 0

If T=2π((L/g))^(1/(2 )) and L=100±0.1 cm(limit standard error) T=2.01±0.01 s (limit standard error) Calculate the value of g and its standard error.

$${If}\:{T}=\mathrm{2}\pi\left(\frac{{L}}{{g}}\right)^{\frac{\mathrm{1}}{\mathrm{2}\:}} \:{and} \\ $$$${L}=\mathrm{100}\pm\mathrm{0}.\mathrm{1}\:{cm}\left({limit}\:{standard}\:\right. \\ $$$$\left.{error}\right) \\ $$$${T}=\mathrm{2}.\mathrm{01}\pm\mathrm{0}.\mathrm{01}\:{s}\:\left({limit}\:{standard}\right. \\ $$$$\left.{error}\right) \\ $$$${Calculate}\:{the}\:{value}\:{of}\:{g}\:{and}\:{its} \\ $$$${standard}\:{error}. \\ $$

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