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

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

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limit as x approaches 0 of 2/(x(x-2))

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

diverges

Solution steps

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

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 ( x - 2 )}) = - \infty

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

= diverges

x \to 0 lim (\frac{7 ^{x} - 8 ^{x}}{x})

x \to π lim (\frac{x}{6} - \frac{π}{2})

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

x \to 0 lim (\frac{sin ( 2 \cdot x )}{x})

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