f-t-0-e-xt-x-t-2-dx-with-t-0-1-study-the-set-of-definition-for-f-t-2-study-the-continuity-of-f-3-study-the-derivability-of-f-4-developp-f-at-integr-serie-

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Question Number 62808 by mathmax by abdo last updated on 25/Jun/19

f(t) =∫_0 ^(+∞) (e^(−xt) /((x+t)^2 ))dx with t≥0 1) study the set of definition for f(t) 2)study the continuity of f 3)study the derivability of f 4) developp f at integr serie

$${f}\left({t}\right)\:=\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{e}^{−{xt}} }{\left({x}+{t}\right)^{\mathrm{2}} }{dx}\:\:\:\:{with}\:{t}\geqslant\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{study}\:{the}\:{set}\:{of}\:{definition}\:{for}\:{f}\left({t}\right) \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{continuity}\:{of}\:{f} \\ $$$$\left.\mathrm{3}\right){study}\:{the}\:{derivability}\:{of}\:{f} \\ $$$$\left.\mathrm{4}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$

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f-t-0-e-xt-x-t-2-dx-with-t-0-1-study-the-set-of-definition-for-f-t-2-study-the-continuity-of-f-3-study-the-derivability-of-f-4-developp-f-at-integr-serie-

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