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

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

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

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

diverges

Solution steps

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

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

= diverges

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