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 0

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

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

0

Solution steps

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

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

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

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

= 0

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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 0