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

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

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limit as x approaches 0 of (x-2)e^{-1/x}

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

diverges

Solution steps

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

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

= diverges

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