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

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

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limit as x approaches 0 of x*e^{1/x}

x \to 0 lim (x \cdot 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

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