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

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

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

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

0

Solution steps

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

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

= 0

y = 4 x^{2} - 3

x \to 0 lim (\frac{( 9 x ^{2} - 2 x )}{x})

\frac{d}{d x} (\frac{x ^{2} - 1}{2 x - 3})

\int_{0}^{1} (x - x^{k}) d x

\int \frac{x ^{2} + 1}{x ^{3} + 3 x ^{2} - 4} d x

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