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

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

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

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

diverges

Solution steps

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

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

then the limit does not exist

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

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

= diverges

x \to \infty lim (- e^{0})

x \to 2 lim (\frac{1}{x ^{8.132}})

x \to 1 lim (arctan (x - 1) + 2)

x \to 4 - lim (ln (4 - x))

x \to 0 - lim (ln (x + 1))

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