What is the limit as x approaches 0 of xe^{1/x} ?

The limit as x approaches 0 of xe^{1/x} is diverges

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limit as x approaches 0 of xe^{1/x}

x \to 0 lim (x e^{\frac{1}{x}})

diverges

Solution steps

x \to 0 lim (x e^{\frac{1}{x}})

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

x \to 0 + lim (x e^{\frac{1}{x}}) = \infty

x \to 0 - lim (x e^{\frac{1}{x}}) = 0

= diverges

\int \frac{3}{x ^{2} + 10 x + 29} d x

x \to - 1 lim (\frac{1}{x ^{2} - 2 x - 3})

\frac{\partial}{\partial y} (\frac{x}{y ^{2} + 1})

\frac{\partial}{\partial x} (x^{3} + 4 x^{2} y + 4 x + 2)

x \to 2 - lim (\frac{2}{2 - x})

What is the limit as x approaches 0 of xe^{1/x} ?
The limit as x approaches 0 of xe^{1/x} is diverges