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}}}) = - \infty

= diverges

x \to 0 lim (\frac{x}{2 sin ( 6 x )})

x \to 2 lim (\frac{x - 2}{∣ 2 - x ∣})

x \to 3 lim (\frac{2}{3 - x})

x \to 2 lim (15)

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

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