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

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

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

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

diverges

Solution steps

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

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

= diverges

\int_{0}^{20} x 20 - x d x

\int \frac{e ^{x}}{4} d x

f (x) = \frac{2}{x}, (5, \frac{2}{5})

y^{^{''}} + 12 y^{^{'}} + 35 y = 0

x \to 0 lim (\frac{4 - x}{x ^{2}})

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