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

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

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

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

0

Solution steps

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

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

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

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

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

= 0 \cdot 0

Simplify

= 0

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x \to 1 lim (x ln ∣ x - 1 ∣)

x \to \infty lim (\frac{( x ^{13} )}{e ^{x}})

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

y \to 0 lim (\frac{cos ( y )}{y})

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