What is the limit as x approaches 0 of xe^{1/x}-2 ?

The limit as x approaches 0 of xe^{1/x}-2 is diverges

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limit as x approaches 0 of xe^{1/x}-2

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

diverges

Solution steps

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

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}} - 2) = \infty

x \to 0 - lim (x e^{\frac{1}{x}} - 2) = - 2

= diverges

x \to 5 lim (x^{2} + 9)

x \to \infty lim (\frac{9}{2 x})

x \to 2 lim (2 x^{2} + 5 x - 2)

x \to 0 + lim ((3 x + 1)^{\frac{1}{x}})

x \to - \infty lim (0 - (x))

What is the limit as x approaches 0 of xe^{1/x}-2 ?
The limit as x approaches 0 of xe^{1/x}-2 is diverges