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

x \to 0 + lim (sin (x) ln (8 x))

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

x \to 0 lim (\frac{3 x}{cos ( x )})

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

x \to 0 lim (x^{2} (1 - ln (x)))

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