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

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

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

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

0

Solution steps

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

Apply the Limit Chain Rule:

0

= 0

x \to - 4 lim (\frac{1}{( x + 4 ) ^{2}})

x \to 0 + lim (x^{x^{x}} - 1)

x \to \frac{π}{2} lim ((2 x - π) tan (x))

x \to 1 + lim (tan (x - 1))

x \to 4 lim (\frac{2 x - 4}{x - 1})

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