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Решите задачу:

$1) \lim_{x \to+0} (xe^{ \frac{2}{x} })=0*e^{ \frac{2}{+0} }=0*e^{+\infty}=\{0*\infty\}= \\ \\ = \lim_{x \to+0} (\frac{e^{ \frac{2}{x} }}{ \frac{1}{x}} )= \frac{e^\frac{2}{0}}{\frac{1}{0}} =\{\frac{\infty}{\infty}\}= \\ \\ = \lim_{x \to+0} \frac{(e^{ \frac{2}{x} })'}{ (\frac{1}{x})'} = \lim_{x \to+0} \frac{- \frac{2}{x^2} e^{ \frac{2}{x} }}{- \frac{1}{x^2}} = \lim_{x \to+0}(2e^{ \frac{2}{x} })=2e^ \frac{2}{0} = \\ \\ =2e^\infty=2*\infty=\infty$

$2) \ \ \lim_{x \to-0} (xe^{ \frac{2}{x} })= 0*e^{ \frac{2}{-0} }=0*e^{-\infty}=0* \frac{1}{e^{\infty}} =0* \frac{1}{\infty} =0*0=0$