What is the limit as x approaches 0 of 2/x-1/(e^x-1) ?

The limit as x approaches 0 of 2/x-1/(e^x-1) is diverges

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limit as x approaches 0 of 2/x-1/(e^x-1)

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

diverges

Solution steps

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

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

= diverges

What is the limit as x approaches 0 of 2/x-1/(e^x-1) ?
The limit as x approaches 0 of 2/x-1/(e^x-1) is diverges