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

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

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

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

diverges

Solution steps

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

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

= diverges

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

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

x \to 0 lim (\frac{x}{2} cos (\frac{1}{x}))

x \to \infty lim (- 2, x)

x \to 1 lim (3 x^{2} - 7 x)

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