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

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

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

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

diverges

Solution steps

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

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

= diverges

x \to \infty lim (\frac{3 x + 1}{x + 3})

x \to \infty lim (\frac{x ^{2} - 6}{2 + x - 3 x ^{2}})

x \to \infty lim (\frac{16 x ^{4} + 64 x ^{2} + x ^{2}}{2 x ^{2} - 4})

x \to 2 lim ((\frac{x ^{2} - 3}{x ^{3} - 4 x + 2})^{2})

x \to 4 + lim (\frac{x - 1}{4 - x})

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