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

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

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

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

- \frac{2}{3}

Decimal

- 0.66666 \dots

Solution steps

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

Simplify

\frac{x ^{2} - 2 x}{3 x} : \frac{1}{3} (x - 2)

= x \to 0 lim (\frac{1}{3} (x - 2))

Plug in the value

x = 0

= \frac{1}{3} (0 - 2)

Simplify

\frac{1}{3} (0 - 2) : - \frac{2}{3}

= - \frac{2}{3}

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