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}}) = 0

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

= diverges

\int \frac{x ^{2}}{( x + 1 ) ^{4}} d x

x \to 0 lim (x - \frac{4}{x ^{2}})

\frac{d}{d x} (arcsech (sin (x)))

\int e^{x} x^{4} d x

\frac{d}{d θ} (a^{2} \cdot sin^{2} (θ) + b^{2} \cdot cos^{2} (θ))

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