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

y = (x^{4} - 6 x) e^{x}

\frac{\partial}{\partial x} (\frac{2 x}{x ^{2} + y ^{2} + 16})

\frac{d}{d x} (\frac{cos ( 2 x )}{x})

3 x^{5} x + \frac{7}{x ^{3} x}

\frac{\partial}{\partial x} (ln (\frac{( x + y )}{x - y}))

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