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

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

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

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

diverges

Solution steps

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

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

= diverges

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

x \to 3 + lim (2 x - 1)

x \to 0 + lim (\frac{1}{x} + \frac{1}{∣ x ∣})

x \to 3 lim (\frac{x + 1}{x ^{2} - 4})

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

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