What is the limit as x approaches 0 of e^x 1/x ?

The limit as x approaches 0 of e^x 1/x is diverges

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limit as x approaches 0 of e^x 1/x

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

diverges

Solution steps

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

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

= diverges

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

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

x \to 4 lim (2 x + 3)

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

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

What is the limit as x approaches 0 of e^x 1/x ?
The limit as x approaches 0 of e^x 1/x is diverges