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

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

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

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

diverges

Solution steps

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

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}} - 1) = \infty

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

= diverges

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