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

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

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

x \to 0 lim (x 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

f (x) = 8 x, at x = 16

lo g_{3} (2 x^{2} + 4 x + 3)

n = 1 \sum \infty \frac{9 9 ^{n} ( n ^{5} + 2 )}{n ^{2} 1 0 ^{2 n}}

f (x) = \frac{11}{ln ( x )}

\int \frac{( 2 x ^{2} - 3 )}{( x - 2 ) ( x ^{2} + 4 )} d x

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