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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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