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

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

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

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

diverges

Solution steps

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

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

then the limit does not exist

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

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

= diverges

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