What is the limit as x approaches 0 of x/(x^2-9x) ?

The limit as x approaches 0 of x/(x^2-9x) is -1/9

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limit as x approaches 0 of x/(x^2-9x)

x \to 0 lim (\frac{x}{x ^{2} - 9 x})

- \frac{1}{9}

Decimal

- 0.11111 \dots

Solution steps

x \to 0 lim (\frac{x}{x ^{2} - 9 x})

Simplify

\frac{x}{x ^{2} - 9 x} : \frac{1}{x - 9}

= x \to 0 lim (\frac{1}{x - 9})

Plug in the value

x = 0

= \frac{1}{0 - 9}

Simplify

= - \frac{1}{9}

What is the limit as x approaches 0 of x/(x^2-9x) ?
The limit as x approaches 0 of x/(x^2-9x) is -1/9