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

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

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

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

diverges

Solution steps

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

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

= diverges

w (x) = (x^{2} (2^{x}))^{3}

\int e^{x^{2}} x d x

\int 120 x (2 x + 1)^{4} d x

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

x \to - 5 + lim (\frac{∣ x - 5 ∣}{x - 5})

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