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let-x-gt-0-and-f-x-x-e-t-t-dt-1-calculate-f-x-2-find-lim-x-xf-x-and-lim-x-0-xf-x-




Question Number 32721 by caravan msup abdo. last updated on 31/Mar/18
let x>0 and f(x)=∫_x ^(+∞)   (e^(−t) /t)dt  1)calculate f^′ (x)  2) find lim_(x→+∞) xf(x) and lim_(x→0^+ ) xf(x).
$${let}\:{x}>\mathrm{0}\:{and}\:{f}\left({x}\right)=\int_{{x}} ^{+\infty} \:\:\frac{{e}^{−{t}} }{{t}}{dt} \\ $$$$\left.\mathrm{1}\right){calculate}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{x}\rightarrow+\infty} {xf}\left({x}\right)\:{and}\:{lim}_{{x}\rightarrow\mathrm{0}^{+} } {xf}\left({x}\right). \\ $$

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