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

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

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

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

diverges

Solution steps

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

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

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

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

= diverges

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

x \to 4 lim (4 x^{3} - 3 x - 5)

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

x \to 5 + lim (\frac{x}{x ^{2} - 25})

x \to 8 - lim (- \frac{7}{x ^{2} - 8 x})

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