What is the limit as x approaches 0 of (x-2)/(3x) ?

The limit as x approaches 0 of (x-2)/(3x) is diverges

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limit as x approaches 0 of (x-2)/(3x)

x \to 0 lim (\frac{x - 2}{3 x})

diverges

Solution steps

x \to 0 lim (\frac{x - 2}{3 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{x - 2}{3 x}) = - \infty

x \to 0 - lim (\frac{x - 2}{3 x}) = \infty

= diverges

x \to - 1 lim (\frac{3 x}{2 x + 2})

x \to 2 lim (\frac{x - 2}{x + 1})

x \to 0 lim (\frac{5 ^{x}}{x})

x \to 0 + lim (4 (sin (x))^{x})

x \to 0 + lim (\frac{ln ( 5 x )}{x})

What is the limit as x approaches 0 of (x-2)/(3x) ?
The limit as x approaches 0 of (x-2)/(3x) is diverges