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

The limit as x approaches 0 of x^2e^{x^{-2}} is infinity

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limit as x approaches 0 of x^2e^{x^{-2}}

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

\infty

Solution steps

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

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

= \infty

What is the limit as x approaches 0 of x^2e^{x^{-2}} ?
The limit as x approaches 0 of x^2e^{x^{-2}} is infinity